Write the standard form of the equation of the parabola that has a vertex at $( - 8 , - 3 )$ and passes through the point $( - 6,2 )$
A) $f ( x ) = \frac { 5 } { 64 } ( x - 8 ) ^ { 2 } - 3$
B)$f ( x ) = - \frac { 3 } { 64 } ( x + 3 ) ^ { 2 } + 6$
C) $f ( x ) = \frac { 5 } { 4 } ( x + 8 ) ^ { 2 } - 3$
D) $f ( x ) = \frac { 1 } { 2 } ( x + 8 ) ^ { 2 } - 6$
E) $f ( x ) = \frac { 1 } { 2 } ( x + 3 ) ^ { 2 } + 2$

Question

Write the standard form of the equation of the parabola that has a vertex at $( - 8 , - 3 )$ and passes through the point $( - 6,2 )$ 
A) $f ( x ) = \frac { 5 } { 64 } ( x - 8 ) ^ { 2 } - 3$
B)$f ( x ) = - \frac { 3 } { 64 } ( x + 3 ) ^ { 2 } + 6$
C) $f ( x ) = \frac { 5 } { 4 } ( x + 8 ) ^ { 2 } - 3$
D) $f ( x ) = \frac { 1 } { 2 } ( x + 8 ) ^ { 2 } - 6$
E) $f ( x ) = \frac { 1 } { 2 } ( x + 3 ) ^ { 2 } + 2$

Quizplus · Accepted Answer

The vertex form of a parabola is $ f(x) = a(x-h)^2 + k $. Given the vertex $(-8, -3)$, the equation becomes $ f(x) = a(x+8)^2 - 3 $. Using the point $(-6, 2)$, substitute to find $ a $: $ 2 = a(-6+8)^2 - 3 $. Solving gives $ a = \frac{5}{4} $. Thus, the equation is $ f(x) = \frac{5}{4}(x+8)^2 - 3 $.

Write the Standard Form of the Equation of the Parabola (−8,−3)( - 8 , - 3 )(−8,−3)

Write the Standard Form of the Equation of the Parabola $( - 8 , - 3 )$