5 months ago
Q:

Find the vertex of the parabola. g(x)=−x2−8x−7

Accepted Solution

A:

Solution variant #9.

Identify the coefficients $a$ and $b$ of the quadratic function
$\begin{array} { l }a=-1,& b=-8\end{array}$
Find the $x$-coordinate of the vertex by substituting $a=-1$ and $b=-8$ into $x=-\frac{ b }{ 2a }$
$x=-\frac{ -8 }{ 2 \times \left( -1 \right) }$
Solve the equation for $x$
$x=-4$
Find the $y$-coordinate of the vertex by evaluating the function for $x=-4$
$\begin{array} { l }g\left( x \right)=-{x}^{2}-8x-7,& x=-4\end{array}$
Calculate the function value for $x=-4$
$g\left( -4 \right)=9$
The vertex of the graph of the quadratic function is at $\left( -4, 9\right)$
$\left( -4, 9\right)$