5 8 modeling with quadratic functions
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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=ax 2 +bx+c Vertex Form y=a(x-h) 2 +k

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5.8 Modeling with Quadratic Functions

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5 8 modeling with quadratic functions

5.8 Modeling with Quadratic Functions

By: L. Keali’i Alicea


Goals

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

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)


5 8 modeling with quadratic functions

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!


5 8 modeling with quadratic functions

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)


5 8 modeling with quadratic functions

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

Assignment

  • 5.8 A (all)


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