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Write a quadratic function for the graph that contains (–4, 0), (–2, –2), and (2, 0).

User Arminda
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1 Answer

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Explanation:

a quadratic equation has 2 zeros.

luckily we got 2 points with y = 0, so these define the zero points.

a quadratic function is usually looking like

ax² + bx + c = 0

and with the zeros being the factors, we get

y = a(x - z1)(x - z2) = a(x + 4)(x - 2) =

= a(x² - 2x + 4x - 8) = a(x² + 2x - 8)

to get "a" we use the third point.

-2 = a((-2)² + 2×-2 - 8) = a(4 - 4 - 8) = -8a

a = -2/-8 = 1/4

and the equation is

y = (1/4)x² + (1/2)x - 8/4 = (1/4)x² + (1/2)x - 2

User Thijs Feryn
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