1. 5.8 Modeling with Quadratic Functions
OBJ: To write quadratic functions given characteristics of their graphs
5.8 Modeling with Quadratic Functions
Do Now:
What are the three “forms” of quadratic equations?

2. Remember the 3 forms of a quadratic equation!
Standard Form y=ax2+bx+c
Vertex Form y=a(x-h)2+k
Intercepts Form y=a(x-p)(x-q)

3. Since you know the vertex, use vertex form! y=a(x-h)2+k
Ex 1: Write a quadratic function for a parabola with a vertex of (-2,1) that passes through the point (1,-1).
Since you know the vertex, use vertex form! y=a(x-h)2+k
Plug the vertex in for (h,k) and the other point in for (x,y). Then, solve for a.
-1=a(1-(-2))2+1
-1=a(3)2+1
-2=9a
Now plug in a, h, & k!

4. Intercept Form: y=a(x-p)(x-q)
Ex 2: Write a quadratic function for a parabola with x-intercepts (1,0) & (4,0) that passes through the point (2,-6).
Intercept Form: y=a(x-p)(x-q)
Plug the intercepts in for p & q and the point in for (x, y). Then, solve for a.
-6=a(2-1)(2-4)
-6=a(1)(-2)
-6=-2a
3=a
Now plug in a, p, & q!
y=3(x-1)(x-4)

5. Standard Form: ax2+bx+c=y
Ex 3: Write a quadratic equation whose graph passes through the points (-3,-4), (-1,0), & (9,-10).
Standard Form: ax2+bx+c=y
Since you are given three points that could be plugged in for x & y, write three eqns. with three variables (a,b,c), then solve using your method of choice such as linear combo, inverse matrices, or Cramer’s rule.
1. a(-3)2+b(-3)+c=-4
2. a(-1)2+b(-1)+c=0
3. a(9)2+b(9)+c=-10
A-1 * B = X =a =b =c