Question

The equation of a parabola is y=2x^2 +8x +3

Write the equation in vertex form and show your work.

Answer 1

Answer: y = 2(x + 2)² - 5

Explanation:

We are going to use the completing the square method to transform this quadratic equation from standard form to vertex form.

Given:

y = 2x² + 8x + 3

Factor the 2 out of the first two terms:

y = 2(x² + 4x) + 3

Add and subtract
`(b)/(2) ^2`:

y = 2(x² + 4x + 4 - 4) + 3

Distribute the 2 into -4 and combine with the 3:

y = 2(x² + 4x + 4) - 5

Factor (x² + 4x + 4):

y = 2(x + 2)² - 5