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5.8 Modeling with Quadratic Functions

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5.8 Modeling with Quadratic Functions

By: L. Keali’i Alicea

- Write quadratic functions given characteristics of their graphs.
- Use technology to find quadratic models for data.

- Standard Form
- y=ax2+bx+c

- Vertex Form
- y=a(x-h)2+k

- Intercepts Form
- y=a(x-p)(x-q)

- 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!

- Intercept Form: y=a(x-p)(x-q)
- Plug the intercepts in for p & q and the point in for x & y.
- -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)

- 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

- 5.8 A (all)