quadtric function storyboard
Snemalna Knjiga Besedilo
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- Today I am going to go over the quadratic function
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- A quadratic equation is a polynomial of degree 2 written as f(x) = ax² + bx + c, where a ≠ 0.
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- On a graph this is shown as a U-shaped curve called a parabola
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- Quadratic functions also have key features, including a vertex at the lowest or highest point, an axis of symmetry (a vertical line through the vertex), and intercepts, including a y-intercept and zero, one, or two x-intercepts where the graph may cross the x-axis
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- To find the vertex, we use the formula x = -b / 2a. This gives us the x-value of the vertex. Then, we plug that value back into the function to find the y-value.
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- But to find the y-intercept, we simply plug in x = 0 into the function. But to find the x-intercept , we set the function equal to zero and solve. We can do this by factoring if possible, or by using the quadratic formula: x = [-b ± √(b² - 4ac)] / 2a.
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- Quadratic functions can be written in different forms.Standard form, f(x) = ax² + bx + c, is the most common.Vertex form, f(x) = a(x - h)² + k, shows the vertex.Intercept form, f(x) = a(x - p)(x - q), shows the x-intercepts.
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- The domain of a quadratic function is all real numbers, because you can plug in any value for x. but the range depends on how the parabola opens whioch If it opens upward, the vertex is the minimum, so y is greater than or equal to that value. but if opens downward, the vertex is the maximum, so y is less than or equal to that value.
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- In conclusion we went over how to identify the key features, find the vertex and intercepts, and use different forms to understand them.
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