# How do you find the vertex and the intercepts for #e(x) = -x² - 8x - 16#?

##### 1 Answer

The vertex is

There are no x-intercepts.

#### Explanation:

Given:

where:

**Vertex:** minimum or maximum point of the parabola

The x-coordinate of the vertex is found using the formula:

Substitute

**The vertex is #(-4,0)#.**

Use the discriminant (D) from the quadratic formula to determine whether there are any x-intercepts.

Plug in the known values.

Since the discriminant is the square root of a negative number, there are no real solutions (x-intercepts).

You could determine the y-intercept and the point opposite the y-intercept to help graph the parabola.

**Y-intercept:** value of

Substitute

**The y-intercept is #(0,-16)#**

**Opposite point**

Substitute

**The opposite point is #(-8,-16)#**

Plot the vertex, y-intercept, and opposite point. Sketch a parabola through the points. Do not connect the dots.

graph{-x^2-8x-16 [-10, 10, -5, 5]}