4.10 Write Quadratic Functions and Models

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Presentation transcript:

4.10 Write Quadratic Functions and Models

In Lessons 4.1 & 4.2 you learned how to graph a given quadratic function. In this lesson you will write quadratic functions when given information about their graphs.

For example, here’s a parabola For example, here’s a parabola. Notice the coordinates of the vertex and a point on the graph are given. (4, 1) Start with Vertex (2, -3) Now use the other given point (4, 1) as replacements for (x,y) a = 1 Thus a quadratic function for the parabola is

3 -2 (-1,2) y = a(x – p)(x – q) 2 = a(-1 +2)(-1 – 3) Write the equation of this parabola. (-1,2) Notice the x-intercepts of the parabola. 3 -2 Start with the intercept form: y = a(x – p)(x – q) y = a(x – -2)(x – 3) Now use the coordinates of a point (-1, 2) and substitute them for (x,y) and solve for a. 2 = a(-1 +2)(-1 – 3) a = -1/2