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Create your own at Storyboard That

Do you know what a quadratic formula is?

x=

−b±√b2−4ac
2a
where the values of a, b, and c are substituted from the quadratic equation ax2 + bx + c = 0.

That looks hard.

It's not o hard. Let's try a problem. We will start with the following: First we want to write the equation in standard form and identify a, b, c

0=x^2+4x+1

This is in standard form.

a=1,b=4,c=1


x=

−b±√b2−4ac

2a


a = 1, b = 4, c = 1

x=

−(4)±√42−4(1)(1)

2(1)


Substitute the values for a,b,c into the quadratic formula

Simplify using the order of operations


x=

−4+√12

2


x=

−4−√12
2

Separate the equation into 2 equations


x=

−(4)±√42−4(1)(1)

2(1)

x=

−(4)±√16−4(1)(1)

2(1)

x=

−(4)±√16−4

2(1)

x=

−(4)±√12

2(1)

x=

−4±√12

2(1)

x=

−4±√12

2




Use your calculator to approximate the square root of 12

x≈

−4+3.46
2

x≈

−4−3.46
2

Simplify each equation


x
−4+3.46
2
−0.54
2
−0.27



x

−4−3.46

2

−7.46

2

−3.73


Compare the approximate solutions to the graph

The two approximate solutions are x = −0.27 and x = −3.73.

The x-intercepts are right where you expected them to be!

That's all there is to it. Was it as hard as you thought?

Not as hard as I thought but it is a lot of work with a lot of steps

I think you did just great and I am sure you are ready for the test.

Thanks. I think so too.

The End!

Create your own at Storyboard That

Do you know what a quadratic formula is?

x=

−b±√b2−4ac
2a
where the values of a, b, and c are substituted from the quadratic equation ax2 + bx + c = 0.

That looks hard.

It's not o hard. Let's try a problem. We will start with the following: First we want to write the equation in standard form and identify a, b, c

0=x^2+4x+1

This is in standard form.

a=1,b=4,c=1


x=

−b±√b2−4ac

2a


a = 1, b = 4, c = 1

x=

−(4)±√42−4(1)(1)

2(1)


Substitute the values for a,b,c into the quadratic formula

Simplify using the order of operations


x=

−4+√12

2


x=

−4−√12
2

Separate the equation into 2 equations


x=

−(4)±√42−4(1)(1)

2(1)

x=

−(4)±√16−4(1)(1)

2(1)

x=

−(4)±√16−4

2(1)

x=

−(4)±√12

2(1)

x=

−4±√12

2(1)

x=

−4±√12

2




Use your calculator to approximate the square root of 12

x≈

−4+3.46
2

x≈

−4−3.46
2

Simplify each equation


x
−4+3.46
2
−0.54
2
−0.27



x

−4−3.46

2

−7.46

2

−3.73


Compare the approximate solutions to the graph

The two approximate solutions are x = −0.27 and x = −3.73.

The x-intercepts are right where you expected them to be!

That's all there is to it. Was it as hard as you thought?

Not as hard as I thought but it is a lot of work with a lot of steps

I think you did just great and I am sure you are ready for the test.

Thanks. I think so too.

The End!

Create your own at Storyboard That

Do you know what a quadratic formula is?

x=

−b±√b2−4ac
2a
where the values of a, b, and c are substituted from the quadratic equation ax2 + bx + c = 0.

That looks hard.

It's not o hard. Let's try a problem. We will start with the following: First we want to write the equation in standard form and identify a, b, c

0=x^2+4x+1

This is in standard form.

a=1,b=4,c=1


x=

−b±√b2−4ac

2a


a = 1, b = 4, c = 1

x=

−(4)±√42−4(1)(1)

2(1)


Substitute the values for a,b,c into the quadratic formula

Simplify using the order of operations


x=

−4+√12

2


x=

−4−√12
2

Separate the equation into 2 equations


x=

−(4)±√42−4(1)(1)

2(1)

x=

−(4)±√16−4(1)(1)

2(1)

x=

−(4)±√16−4

2(1)

x=

−(4)±√12

2(1)

x=

−4±√12

2(1)

x=

−4±√12

2




Use your calculator to approximate the square root of 12

x≈

−4+3.46
2

x≈

−4−3.46
2

Simplify each equation


x
−4+3.46
2
−0.54
2
−0.27



x

−4−3.46

2

−7.46

2

−3.73


Compare the approximate solutions to the graph

The two approximate solutions are x = −0.27 and x = −3.73.

The x-intercepts are right where you expected them to be!

That's all there is to it. Was it as hard as you thought?

Not as hard as I thought but it is a lot of work with a lot of steps

I think you did just great and I am sure you are ready for the test.

Thanks. I think so too.

The End!

Create your own at Storyboard That

Do you know what a quadratic formula is?

x=

−b±√b2−4ac
2a
where the values of a, b, and c are substituted from the quadratic equation ax2 + bx + c = 0.

That looks hard.

It's not o hard. Let's try a problem. We will start with the following: First we want to write the equation in standard form and identify a, b, c

0=x^2+4x+1

This is in standard form.

a=1,b=4,c=1


x=

−b±√b2−4ac

2a


a = 1, b = 4, c = 1

x=

−(4)±√42−4(1)(1)

2(1)


Substitute the values for a,b,c into the quadratic formula

Simplify using the order of operations


x=

−4+√12

2


x=

−4−√12
2

Separate the equation into 2 equations


x=

−(4)±√42−4(1)(1)

2(1)

x=

−(4)±√16−4(1)(1)

2(1)

x=

−(4)±√16−4

2(1)

x=

−(4)±√12

2(1)

x=

−4±√12

2(1)

x=

−4±√12

2




Use your calculator to approximate the square root of 12

x≈

−4+3.46
2

x≈

−4−3.46
2

Simplify each equation


x
−4+3.46
2
−0.54
2
−0.27



x

−4−3.46

2

−7.46

2

−3.73


Compare the approximate solutions to the graph

The two approximate solutions are x = −0.27 and x = −3.73.

The x-intercepts are right where you expected them to be!

That's all there is to it. Was it as hard as you thought?

Not as hard as I thought but it is a lot of work with a lot of steps

I think you did just great and I am sure you are ready for the test.

Thanks. I think so too.

The End!

Create your own at Storyboard That

Do you know what a quadratic formula is?

x=

−b±√b2−4ac
2a
where the values of a, b, and c are substituted from the quadratic equation ax2 + bx + c = 0.

That looks hard.

It's not o hard. Let's try a problem. We will start with the following: First we want to write the equation in standard form and identify a, b, c

0=x^2+4x+1

This is in standard form.

a=1,b=4,c=1


x=

−b±√b2−4ac

2a


a = 1, b = 4, c = 1

x=

−(4)±√42−4(1)(1)

2(1)


Substitute the values for a,b,c into the quadratic formula

Simplify using the order of operations


x=

−4+√12

2


x=

−4−√12
2

Separate the equation into 2 equations


x=

−(4)±√42−4(1)(1)

2(1)

x=

−(4)±√16−4(1)(1)

2(1)

x=

−(4)±√16−4

2(1)

x=

−(4)±√12

2(1)

x=

−4±√12

2(1)

x=

−4±√12

2




Use your calculator to approximate the square root of 12

x≈

−4+3.46
2

x≈

−4−3.46
2

Simplify each equation


x
−4+3.46
2
−0.54
2
−0.27



x

−4−3.46

2

−7.46

2

−3.73


Compare the approximate solutions to the graph

The two approximate solutions are x = −0.27 and x = −3.73.

The x-intercepts are right where you expected them to be!

That's all there is to it. Was it as hard as you thought?

Not as hard as I thought but it is a lot of work with a lot of steps

I think you did just great and I am sure you are ready for the test.

Thanks. I think so too.

The End!

Create your own at Storyboard That

Do you know what a quadratic formula is?

x=

−b±√b2−4ac
2a
where the values of a, b, and c are substituted from the quadratic equation ax2 + bx + c = 0.

That looks hard.

It's not o hard. Let's try a problem. We will start with the following: First we want to write the equation in standard form and identify a, b, c

0=x^2+4x+1

This is in standard form.

a=1,b=4,c=1


x=

−b±√b2−4ac

2a


a = 1, b = 4, c = 1

x=

−(4)±√42−4(1)(1)

2(1)


Substitute the values for a,b,c into the quadratic formula

Simplify using the order of operations


x=

−4+√12

2


x=

−4−√12
2

Separate the equation into 2 equations


x=

−(4)±√42−4(1)(1)

2(1)

x=

−(4)±√16−4(1)(1)

2(1)

x=

−(4)±√16−4

2(1)

x=

−(4)±√12

2(1)

x=

−4±√12

2(1)

x=

−4±√12

2




Use your calculator to approximate the square root of 12

x≈

−4+3.46
2

x≈

−4−3.46
2

Simplify each equation


x
−4+3.46
2
−0.54
2
−0.27



x

−4−3.46

2

−7.46

2

−3.73


Compare the approximate solutions to the graph

The two approximate solutions are x = −0.27 and x = −3.73.

The x-intercepts are right where you expected them to be!

That's all there is to it. Was it as hard as you thought?

Not as hard as I thought but it is a lot of work with a lot of steps

I think you did just great and I am sure you are ready for the test.

Thanks. I think so too.

The End!

Create your own at Storyboard That

Do you know what a quadratic formula is?

x=

−b±√b2−4ac
2a
where the values of a, b, and c are substituted from the quadratic equation ax2 + bx + c = 0.

That looks hard.

It's not o hard. Let's try a problem. We will start with the following: First we want to write the equation in standard form and identify a, b, c

0=x^2+4x+1

This is in standard form.

a=1,b=4,c=1


x=

−b±√b2−4ac

2a


a = 1, b = 4, c = 1

x=

−(4)±√42−4(1)(1)

2(1)


Substitute the values for a,b,c into the quadratic formula

Simplify using the order of operations


x=

−4+√12

2


x=

−4−√12
2

Separate the equation into 2 equations


x=

−(4)±√42−4(1)(1)

2(1)

x=

−(4)±√16−4(1)(1)

2(1)

x=

−(4)±√16−4

2(1)

x=

−(4)±√12

2(1)

x=

−4±√12

2(1)

x=

−4±√12

2




Use your calculator to approximate the square root of 12

x≈

−4+3.46
2

x≈

−4−3.46
2

Simplify each equation


x
−4+3.46
2
−0.54
2
−0.27



x

−4−3.46

2

−7.46

2

−3.73


Compare the approximate solutions to the graph

The two approximate solutions are x = −0.27 and x = −3.73.

The x-intercepts are right where you expected them to be!

That's all there is to it. Was it as hard as you thought?

Not as hard as I thought but it is a lot of work with a lot of steps

I think you did just great and I am sure you are ready for the test.

Thanks. I think so too.

The End!

Create your own at Storyboard That

Do you know what a quadratic formula is?

x=

−b±√b2−4ac
2a
where the values of a, b, and c are substituted from the quadratic equation ax2 + bx + c = 0.

That looks hard.

It's not o hard. Let's try a problem. We will start with the following: First we want to write the equation in standard form and identify a, b, c

0=x^2+4x+1

This is in standard form.

a=1,b=4,c=1


x=

−b±√b2−4ac

2a


a = 1, b = 4, c = 1

x=

−(4)±√42−4(1)(1)

2(1)


Substitute the values for a,b,c into the quadratic formula

Simplify using the order of operations


x=

−4+√12

2


x=

−4−√12
2

Separate the equation into 2 equations


x=

−(4)±√42−4(1)(1)

2(1)

x=

−(4)±√16−4(1)(1)

2(1)

x=

−(4)±√16−4

2(1)

x=

−(4)±√12

2(1)

x=

−4±√12

2(1)

x=

−4±√12

2




Use your calculator to approximate the square root of 12

x≈

−4+3.46
2

x≈

−4−3.46
2

Simplify each equation


x
−4+3.46
2
−0.54
2
−0.27



x

−4−3.46

2

−7.46

2

−3.73


Compare the approximate solutions to the graph

The two approximate solutions are x = −0.27 and x = −3.73.

The x-intercepts are right where you expected them to be!

That's all there is to it. Was it as hard as you thought?

Not as hard as I thought but it is a lot of work with a lot of steps

I think you did just great and I am sure you are ready for the test.

Thanks. I think so too.

The End!

Create your own at Storyboard That

Do you know what a quadratic formula is?

x=

−b±√b2−4ac
2a
where the values of a, b, and c are substituted from the quadratic equation ax2 + bx + c = 0.

That looks hard.

It's not o hard. Let's try a problem. We will start with the following: First we want to write the equation in standard form and identify a, b, c

0=x^2+4x+1

This is in standard form.

a=1,b=4,c=1


x=

−b±√b2−4ac

2a


a = 1, b = 4, c = 1

x=

−(4)±√42−4(1)(1)

2(1)


Substitute the values for a,b,c into the quadratic formula

Simplify using the order of operations


x=

−4+√12

2


x=

−4−√12
2

Separate the equation into 2 equations


x=

−(4)±√42−4(1)(1)

2(1)

x=

−(4)±√16−4(1)(1)

2(1)

x=

−(4)±√16−4

2(1)

x=

−(4)±√12

2(1)

x=

−4±√12

2(1)

x=

−4±√12

2




Use your calculator to approximate the square root of 12

x≈

−4+3.46
2

x≈

−4−3.46
2

Simplify each equation


x
−4+3.46
2
−0.54
2
−0.27



x

−4−3.46

2

−7.46

2

−3.73


Compare the approximate solutions to the graph

The two approximate solutions are x = −0.27 and x = −3.73.

The x-intercepts are right where you expected them to be!

That's all there is to it. Was it as hard as you thought?

Not as hard as I thought but it is a lot of work with a lot of steps

I think you did just great and I am sure you are ready for the test.

Thanks. I think so too.

The End!

Create your own at Storyboard That

Do you know what a quadratic formula is?

x=

−b±√b2−4ac
2a
where the values of a, b, and c are substituted from the quadratic equation ax2 + bx + c = 0.

That looks hard.

It's not o hard. Let's try a problem. We will start with the following: First we want to write the equation in standard form and identify a, b, c

0=x^2+4x+1

This is in standard form.

a=1,b=4,c=1


x=

−b±√b2−4ac

2a


a = 1, b = 4, c = 1

x=

−(4)±√42−4(1)(1)

2(1)


Substitute the values for a,b,c into the quadratic formula

Simplify using the order of operations


x=

−4+√12

2


x=

−4−√12
2

Separate the equation into 2 equations


x=

−(4)±√42−4(1)(1)

2(1)

x=

−(4)±√16−4(1)(1)

2(1)

x=

−(4)±√16−4

2(1)

x=

−(4)±√12

2(1)

x=

−4±√12

2(1)

x=

−4±√12

2




Use your calculator to approximate the square root of 12

x≈

−4+3.46
2

x≈

−4−3.46
2

Simplify each equation


x
−4+3.46
2
−0.54
2
−0.27



x

−4−3.46

2

−7.46

2

−3.73


Compare the approximate solutions to the graph

The two approximate solutions are x = −0.27 and x = −3.73.

The x-intercepts are right where you expected them to be!

That's all there is to it. Was it as hard as you thought?

Not as hard as I thought but it is a lot of work with a lot of steps

I think you did just great and I am sure you are ready for the test.

Thanks. I think so too.

The End!

Create your own at Storyboard That

Do you know what a quadratic formula is?

x=

−b±√b2−4ac
2a
where the values of a, b, and c are substituted from the quadratic equation ax2 + bx + c = 0.

That looks hard.

It's not o hard. Let's try a problem. We will start with the following: First we want to write the equation in standard form and identify a, b, c

0=x^2+4x+1

This is in standard form.

a=1,b=4,c=1


x=

−b±√b2−4ac

2a


a = 1, b = 4, c = 1

x=

−(4)±√42−4(1)(1)

2(1)


Substitute the values for a,b,c into the quadratic formula

Simplify using the order of operations


x=

−4+√12

2


x=

−4−√12
2

Separate the equation into 2 equations


x=

−(4)±√42−4(1)(1)

2(1)

x=

−(4)±√16−4(1)(1)

2(1)

x=

−(4)±√16−4

2(1)

x=

−(4)±√12

2(1)

x=

−4±√12

2(1)

x=

−4±√12

2




Use your calculator to approximate the square root of 12

x≈

−4+3.46
2

x≈

−4−3.46
2

Simplify each equation


x
−4+3.46
2
−0.54
2
−0.27



x

−4−3.46

2

−7.46

2

−3.73


Compare the approximate solutions to the graph

The two approximate solutions are x = −0.27 and x = −3.73.

The x-intercepts are right where you expected them to be!

That's all there is to it. Was it as hard as you thought?

Not as hard as I thought but it is a lot of work with a lot of steps

I think you did just great and I am sure you are ready for the test.

Thanks. I think so too.

The End!

Create your own at Storyboard That

Do you know what a quadratic formula is?

x=

−b±√b2−4ac
2a
where the values of a, b, and c are substituted from the quadratic equation ax2 + bx + c = 0.

That looks hard.

It's not o hard. Let's try a problem. We will start with the following: First we want to write the equation in standard form and identify a, b, c

0=x^2+4x+1

This is in standard form.

a=1,b=4,c=1


x=

−b±√b2−4ac

2a


a = 1, b = 4, c = 1

x=

−(4)±√42−4(1)(1)

2(1)


Substitute the values for a,b,c into the quadratic formula

Simplify using the order of operations


x=

−4+√12

2


x=

−4−√12
2

Separate the equation into 2 equations


x=

−(4)±√42−4(1)(1)

2(1)

x=

−(4)±√16−4(1)(1)

2(1)

x=

−(4)±√16−4

2(1)

x=

−(4)±√12

2(1)

x=

−4±√12

2(1)

x=

−4±√12

2




Use your calculator to approximate the square root of 12

x≈

−4+3.46
2

x≈

−4−3.46
2

Simplify each equation


x
−4+3.46
2
−0.54
2
−0.27



x

−4−3.46

2

−7.46

2

−3.73


Compare the approximate solutions to the graph

The two approximate solutions are x = −0.27 and x = −3.73.

The x-intercepts are right where you expected them to be!

That's all there is to it. Was it as hard as you thought?

Not as hard as I thought but it is a lot of work with a lot of steps

I think you did just great and I am sure you are ready for the test.

Thanks. I think so too.

The End!

Create your own at Storyboard That

Do you know what a quadratic formula is?

x=

−b±√b2−4ac
2a
where the values of a, b, and c are substituted from the quadratic equation ax2 + bx + c = 0.

That looks hard.

It's not o hard. Let's try a problem. We will start with the following: First we want to write the equation in standard form and identify a, b, c

0=x^2+4x+1

This is in standard form.

a=1,b=4,c=1


x=

−b±√b2−4ac

2a


a = 1, b = 4, c = 1

x=

−(4)±√42−4(1)(1)

2(1)


Substitute the values for a,b,c into the quadratic formula

Simplify using the order of operations


x=

−4+√12

2


x=

−4−√12
2

Separate the equation into 2 equations


x=

−(4)±√42−4(1)(1)

2(1)

x=

−(4)±√16−4(1)(1)

2(1)

x=

−(4)±√16−4

2(1)

x=

−(4)±√12

2(1)

x=

−4±√12

2(1)

x=

−4±√12

2




Use your calculator to approximate the square root of 12

x≈

−4+3.46
2

x≈

−4−3.46
2

Simplify each equation


x
−4+3.46
2
−0.54
2
−0.27



x

−4−3.46

2

−7.46

2

−3.73


Compare the approximate solutions to the graph

The two approximate solutions are x = −0.27 and x = −3.73.

The x-intercepts are right where you expected them to be!

That's all there is to it. Was it as hard as you thought?

Not as hard as I thought but it is a lot of work with a lot of steps

I think you did just great and I am sure you are ready for the test.

Thanks. I think so too.

The End!

Create your own at Storyboard That

Do you know what a quadratic formula is?

x=

−b±√b2−4ac
2a
where the values of a, b, and c are substituted from the quadratic equation ax2 + bx + c = 0.

That looks hard.

It's not o hard. Let's try a problem. We will start with the following: First we want to write the equation in standard form and identify a, b, c

0=x^2+4x+1

This is in standard form.

a=1,b=4,c=1


x=

−b±√b2−4ac

2a


a = 1, b = 4, c = 1

x=

−(4)±√42−4(1)(1)

2(1)


Substitute the values for a,b,c into the quadratic formula

Simplify using the order of operations


x=

−4+√12

2


x=

−4−√12
2

Separate the equation into 2 equations


x=

−(4)±√42−4(1)(1)

2(1)

x=

−(4)±√16−4(1)(1)

2(1)

x=

−(4)±√16−4

2(1)

x=

−(4)±√12

2(1)

x=

−4±√12

2(1)

x=

−4±√12

2




Use your calculator to approximate the square root of 12

x≈

−4+3.46
2

x≈

−4−3.46
2

Simplify each equation


x
−4+3.46
2
−0.54
2
−0.27



x

−4−3.46

2

−7.46

2

−3.73


Compare the approximate solutions to the graph

The two approximate solutions are x = −0.27 and x = −3.73.

The x-intercepts are right where you expected them to be!

That's all there is to it. Was it as hard as you thought?

Not as hard as I thought but it is a lot of work with a lot of steps

I think you did just great and I am sure you are ready for the test.

Thanks. I think so too.

The End!

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Storyboard Text

  • Slide: 1
  • Do you know what a quadratic formula is?
  • Slide: 2
  • x=−b±√b2−4ac2awhere the values of a, b, and c are substituted from the quadratic equation ax2+ bx + c = 0.
  • That looks hard.
  • Slide: 3
  • It's not o hard. Let's try a problem. We will start with the following: First we want to write the equation in standard form and identify a, b, c0=x^2+4x+1This is in standard form.a=1,b=4,c=1
  • Slide: 4
  • x= −b±√b2−4ac 2a a = 1,b = 4,c = 1x= −(4)±√42−4(1)(1) 2(1)
  • Substitute the values for a,b,c into the quadratic formula
  • Slide: 5
  • x= −(4)±√42−4(1)(1) 2(1) x= −(4)±√16−4(1)(1) 2(1) x= −(4)±√16−4 2(1) x= −(4)±√12 2(1) x= −4±√12 2(1) x= −4±√12 2 
  • Simplify using the order of operations
  • Slide: 6
  • x= −4+√12 2
  • x=−4−√122
  • Separate the equation into 2 equations
  • Slide: 7
  • x≈−4+3.462
  • x≈−4−3.462
  • Use your calculator to approximate the square root of 12
  • Slide: 8
  • x ≈ −4−3.46 2 ≈ −7.46 2 ≈ −3.73
  • Simplify each equation
  • x≈−4+3.462≈−0.542≈−0.27
  • Slide: 9
  • The two approximate solutions arex = −0.27andx = −3.73.
  • The x-intercepts are right where you expected them to be!
  • Compare the approximate solutions to the graph
  • Slide: 10
  • That's all there is to it. Was it as hard as you thought?
  • Not as hard as I thought but it is a lot of work with a lot of steps
  • Slide: 11
  • I think you did just great and I am sure you are ready for the test.
  • Thanks. I think so too.
  • Slide: 12
  • The End!
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