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The graph of quadratic function f has zeros of -8 and 4 and a maximum at (-2,18). What is the value of a in the function’s equation?

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Theleangreenbeanidn

Quadratic Function Equations

To find the equation of a parabola given the vertex and the zeroes, we can use the intercept form equation to help us:

[tex]y=a(x-r)(x-s)[/tex]

  • r and s = intercepts/zeros of the graph

Solving the Question

We're given:

  • Zeros: -8, 4
  • Maximum: (-2, 18)

[tex]y=a(x-r)(x-s)[/tex]

⇒ Plug in the given information:

[tex]y=a(x-(-8))(x-4)\\18=a(-2-(-8))(-2-4)\\18=a(-2+8)(-2-4)\\18=a(6)(-6)\\18=a(-36)\\1=-2a\\\\a=-\dfrac{1}{2}[/tex]

Answer

[tex]a=-\dfrac{1}{2}[/tex]

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