Find an equation of the parabola that has a vertex at $( - 5 , - 7 )$ and whose graph passes through the point $( - 6 , - 10 ).$
A) $y = 3 ( x + 7 ) ^ { 2 } - 5$
B) $y = - 3 ( x + 5 ) ^ { 2 } - 7$
C) $y = 3 ( x - 5 ) ^ { 2 } - 7$
D) $y = - 3 ( x + 5 ) ^ { 2 } + 7$
E) $y = 3 ( x + 5 ) ^ { 2 } + 7$

Question

Quizplus · Accepted Answer

The general form of a parabola's equation is $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex. Substituting the vertex $(-5, -7)$ into this form gives $y = a(x + 5)^2 - 7$. To find $a$, use the point $(-6, -10)$: $-10 = a(-6 + 5)^2 - 7$. Solving for $a$ gives $a = -3$, so the correct equation is $y = -3(x + 5)^2 - 7$.

Find an Equation of the Parabola That Has a Vertex (−5,−7)( - 5 , - 7 )(−5,−7)

Find an Equation of the Parabola That Has a Vertex $( - 5 , - 7 )$