Question

Question 1 of 10

2 Points
The standard form of the equation of a parabola is y = 7x2 + 14x + 4.
What is the vertex form of the equation?
A. y = 7(x + 1)2-3
B. y= 7(x + 2)2-3
c. y= 7(x + 1)2 + 3
D. y= 7(x + 2)2 + 3
SUBMIT

Answer 1

A. y = 7(x + 1)²-3

Explanation:

Parabola:

`y = 7x^(2) + 14x + 4`

`y = 7(x^(2) + 2x) + 4`

Putting into vertex form, remember that:

`(x + a)^(2) = x^(2) + 2ax + a^(2)`

In this question:

`x^(2) + 2x`, to put into this format:

`x^(2) + 2x + 1 = (x + 1)^(2)`

We add one inside the parenthesis to do this. The parenthesis is multiplied by 7, so for the equivalent, we also have to subtract 7. Then

Vertex form:

`y = 7(x^(2) + 2x + 1) + 4 - 7`

`y = 7(x + 1)^(2) - 3`

So the correct answer is:

A. y = 7(x + 1)²-3