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# 5.8 Modeling with Quadratic Functions - PowerPoint PPT Presentation

5.8 Modeling with Quadratic Functions. By: L. Keali’i Alicea. Goals. Write quadratic functions given characteristics of their graphs. Use technology to find quadratic models for data. Remember the 3 forms of a quadratic equation!. Standard Form y=ax 2 +bx+c Vertex Form y=a(x-h) 2 +k

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### 5.8 Modeling with Quadratic Functions

By: L. Keali’i Alicea

Goals
• Write quadratic functions given characteristics of their graphs.
• Use technology to find quadratic models for data.
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)
Example: Write a quadraticfunction 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!

Example: Write a quadratic function in intercept form 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.
• -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)

Example: Write a quadratic equation in standard form 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

Assignment
• 5.8 A (all)