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Determine an equation of a quadratic function with x-intercepts of 2 and 8, that passes through the point E(10. - 16).

User Roray
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Explanation:

We know that the parabola will be able to be factored into y=a(x+2)(x−3)y=a(x+2)(x−3), where aa will be some scaling factor that restricts the parabola to run through the point (5,10)(5,10). To find aa, just substitute values for xx and y,y,

y=a(x+2)(x−3)∣∣∣(5,10)⟹10=a(5+2)(5−3)y=a(x+2)(x−3)|(5,10)⟹10=a(5+2)(5−3)

We can then conclude that a=57a=57. Thus, our parabola is

f(x)=57x2−57x−307f(x)=57x2−57x−307

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