Question

Find the vertex of the graph of the function: f(x)= -2x^2-16x-34Answer choices:-2,-4-4,-23,55,3

Answer 1

To calculate the vertex of the parabola you have to use the following formula:

Given the function:

`f(x)=ax^2+bx+c`

The x-coordinate of the vertex can be calculated as:

`x_V=-(b)/(2a)`

For the function:

`f(x)=-2x^2-16x-34`

a=-2

b=-16

c=-34

The x-coordinate of the vertex is

`x_V=-((-16))/(2(-2))=-4`

The x-coordinate of the vertex is x=-4

Now to calculate the y-coordinate of the vertex you have to replace the formula with the x-coordinate you just obtained:

`\begin{gathered} y_V=f(x_V)=-2(-4)^2-16\cdot(-4)-34 \\ y_V=-32+64-34 \\ y_V=-2 \end{gathered}`

The coordinates of the vertex are (-4,-2) the correct option is the second one.