1. 4.10 Write Quadratic Functions and Models

2. 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.

3. 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

4. 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