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=(-b)/(2a) \\ x_V=(-(-12))/(2\cdot(-2)) \\ x_V=(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