Question

A quadratic function has x-intercepts at −7 and 1. The vertex of the function is at (−3, 16). What is the equation of the function?

A. f(x) = x2 + 6x − 7
B. f(x) = −x2 − 6x + 7
C. f(x) = x2 − 6x + 7
D. f(x) = −x2 + 6x − 7

Answer 1

`\begin{cases} x = -7 &\implies x +7=0\\ x = 1 &\implies x -1=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +7 )( x -1 ) = \stackrel{0}{y}}\hspace{5em}\textit{we also know that } \begin{cases} x=-3\\ y=16 \end{cases} \\\\\\ a ( -3 +7 )( -3 -1 ) = 16\implies a(4)(-4)=16\implies -16a=16 \\\\\\ a=\cfrac{16}{-16}\implies a=-1 \\\\[-0.35em] ~\dotfill\\\\ -1( x +7 )( x -1 ) =y\implies -(x^2+6x-7)=y\implies \boxed{-x^2-6x+7=y}`

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