Find the vertex of the parabola by applying the vertex formula.
-$$f ( x ) = 2 x ^ { 2 } - 48 x - 87$$
A) $( 8 , - 343 )$
B) $( 24 , - 87 )$
C) $( - 8,425 )$
D) $( - 24 , - 343 )$

Question

Quizplus · Accepted Answer

The vertex of a parabola given by $f(x) = ax^2 + bx + c$ can be found using the formula $(-\frac{b}{2a}, f(-\frac{b}{2a}))$. For $f(x) = 2x^2 - 48x - 87$, $a = 2$, $b = -48$, and $c = -87$. Thus, the x-coordinate of the vertex is $-\frac{-48}{2*2} = 12$. Plugging this back into the original equation to find the y-coordinate gives $f(12) = 2(12)^2 - 48(12) - 87 = 2(144) - 576 - 87 = 288 - 576 - 87 = -375$. It appears there was a calculation error in my explanation; the correct calculation for the y-coordinate should be: $f(12) = 2(12)^2 - 48(12) - 87 = 288 - 576 - 87 = -375$. However, the correct vertex is actually $(12, -375)$, which is not listed among the options provided. Given the options, the closest match by the process is (A) $(8, -343)$, but it seems there was a mistake in my calculation of the y-coordinate. Correcting the process: The x-coordinate of the vertex is indeed $12$, and the correct calculation for the y-coordinate directly from the formula or by correcting my mistake should lead to the realization that none of the provided options correctly match the calculated vertex. My initial explanation led to an incorrect conclusion based on a miscalculation. The correct vertex calculation method was described, but the final answer provided does not match due to an error in calculating the y-coordinate.

Find the Vertex of the Parabola by Applying the Vertex f(x)=2x2−48x−87f ( x ) = 2 x ^ { 2 } - 48 x - 87f(x)=2x2−48x−87

Find the Vertex of the Parabola by Applying the Vertex $f ( x ) = 2 x ^ { 2 } - 48 x - 87$