Question

artis the vertex, aws or symmety a monday value of each 83

Answer 1

$y=-2x^2-12x+3$

This equation has the form:

$y=ax^2+bx+c$

with a = -2, b = -12, and c = 3

The x-coordinate of the vertex is found as follows:

$\begin{gathered} x_V=\frac{-b}{2a} \\ x_V=\frac{-(-12)}{2\cdot(-2)} \\ x_V=\frac{12}{-4} \\ x_V=-3 \end{gathered}$

The y-coordinate of the vertex is found replacing the x-coordinate into the equation:

$\begin{gathered} y_V=-2x^2_V-12x_V+3 \\ y_V=-2(-3)^2-12\cdot(-3)+3 \\ y_V=-18+36+3 \\ y_V=21 \end{gathered}$

vertex: (-3, 21)

The axis of symmetry is:

$\begin{gathered} x=x_V \\ x=-3 \end{gathered}$

Given that a is negative, then the vertex is a maximum