# How do you find the vertex and intercepts for #y = 4x^2 + 8x + 7#?

##### 2 Answers

Therefore, the vertex is

#### Explanation:

Take out the common factor

Complete the square

Simplify

which is in the form

Therefore, the vertex is

For y-intercept, sub

For x-intercept, sub

Therefore, no solution as any number squared is greater than or equal to 0.

graph{4x^2+8x+7 [-10, 10, -5, 5]}

Above is the parabola

Vertex is at

y-intercept is at

(there is no x-intercept)

#### Explanation:

The easiest way (in this case) to find the vertex is to convert the given equation into vertex form:

Given

Extracting the

Completing the square:

Re-writing as a squared binomial and simplifying the constants

Adjusting the sign inside the squared binomial to match the vertex form requirement

which is the vertex form with vertex at

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The y-intercept is the value of

based on the original equation

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The x-intercept is the value of

from our derived vertex form:

but