Find the quadratic function $f$ whose graph intersects the $x$-axis at $( - 7,0 )$ and $( 1,0 )$ and the $y$-axis at $( 0 , - 14 )$.
A) $f ( x ) = - 2 x ^ { 2 } - 16 x - 2$
B) $f ( x ) = 2 x ^ { 2 } + 12 x - 14$
C) $f ( x ) = 2 x ^ { 2 } + 16 x - 7$
D) $f ( x ) = - 2 x ^ { 2 } + 16 x - 14$
E) $f ( x ) = - 2 x ^ { 2 } - 12 x - 14$

Question

Quizplus · Accepted Answer

Since the graph intersects the $y$-axis at $(0,-14)$, the constant term of the quadratic should be $-14$. The given $x$-intercepts are $(-7,0)$ and $(1,0)$, which means the quadratic has roots at $x=-7$ and $x=1$. Hence, the quadratic can be factored as $f(x)=a(x+7)(x-1)$, where $a$ is some nonzero constant. Substituting the point $(0,-14)$ into this equation gives $-14=a(7)(-1)$, so $a=2$. Thus, the quadratic is given by $f(x)=2(x+7)(x-1)=\boxed{\textbf{(B) }f(x) = 2x ^ { 2 } + 12 x - 14}$.

Find the Quadratic Function fff Whose Graph Intersects The xxx -Axis At (−7,0)( - 7,0 )(−7,0)

Find the Quadratic Function $f$ Whose Graph Intersects The $x$ -Axis At $( - 7,0 )$