Pre Calculus Project

Pre Calculus Project
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  • A teacher in class decided to teach a new interesting lesson on a beautiful Sunday morning.
  • Goodmorning class! So today we will learn about quadratic functions
  • The quadratic function is a function of a form, f(x)=ax2+bx+ c, where 'a' can't be equal to 0.
  • Quadratic Functions and Models
  • The students were interested and were engaged in the new lesson.
  • Is the graph of a quadratic function a parabola?
  • This seems interesting!!
  • The teacher started by explaining how to find the standard form of the quadratic formula.
  • Yes. Now for finding the standard form of a quadratic formula, complete the squares by using (-b/2)2
  • 3x2- 6x + 1 3 ( x2 - 2x + _____) + 1 - _____ 3 ( x2 - 2x + 1 ) + 1 - 3 ( 1 ) 3 ( x - 1 )2 - 2
  • Complete the square by adding 1 inside the parenthesis and subtracting 3 x 1 from outside, then you just factor.
  • Then, she taught them how to find the vertex.
  • Vertex
  • To find the vertex we use this standard form, f ( x ) = a ( x - h )2 + k Use points (h,k) as (x,y) to graph the vertex. In the example I gave you, the vertex will be, ( 1, -2 )
  • The teacher then moved on and explained the minimum and maximum value.
  • Now for finding the minimum or maximum value of a quadratic function, the minimum or maximum value of f occurs at x = h.  
  • If a>0, then the minimum value of f is f ( h ) = k, and the parabola is facing upwards. If a<0, then the maximum value of f is f ( h ) = k, and the parabola is facing downwards.
  • The students were interested and they started asking questions.
  • Oh Mrs. Christy, to find the minimum or maximum value do we use (-b/2a) ?
  • Done By: Tala Jomaa
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