# How do you find the vertex and intercepts for #y=8(x-10)^2-16#?

##### 2 Answers

The vertex form of a quadratic function is given by

f (x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola.

So here, it's already in vertex form. a = 8, h = 10, k = -16, and the vertex coordinates are 10, -16

Intercepts can be easily calculated. The y intercept is found when x = 0 is substituted into the original equation:

x intercepts are found by setting y = 0 and solving for x.

...easiest way to solve this is to convert it to a standard format quadratic equation.

Multiply out:

...this is standard form,

a = 8, b = -160, c = 784

giving roots 11.41 and 8.59 (rounded)

...always good to have a graph as function as a sanity check:

graph{8(x - 10)^2 - 16 [-10.51, 21.52, -19.47, -3.45]}

GOOD LUCK!

Vertex is

#### Explanation:

To find the vertex, we should have equation into vertex form i.e.

As

Hence, vertex is

For

Putting

and when

graph{8(x-10)^2-16 [-5, 20, -100, 860]}