Question

The equation 5x2 + 30x + 15 = 0 is being rewritten in vertex form. Fill in the missing step.

Given 5x2 + 30x + 15 = 0
Step 1 ✔
Step 2 5(x2 + 6x + 9) + 15 − 45 = 0
Step 3 5(x + 3)2 − 30 = 0
A: 5(x2 + 30x ___) + 15 ___ = 0
B:5(x2 + 30x ___) − 15 ___ = 0
C:5(x2 + 6x ___) − 15 ___ = 0
D:5(x2 + 6x ___) + 15 ___ = 0

Answer 1

D is right

Explanation:

Took the test

Answer 2

D:5(x2 + 6x ___) + 15 ___ = 0

Explanation:

Parabola in Vertex Form

To express the equation of a parabola in vertex form we must complete squares. The equation is given as

`5x^2 + 30x + 15 = 0`

The first step is to factor 5 and leave space to complete the third term in the parentheses, along with a space outside it to compensate. This should look like

`5(x^2 + 6x\text{........)} + 15....... = 0`

Those spaces need to be filled out like shown in the step 2. Thus the correct option is D