Question

How to convert from standard form to vertex form

Answer 1

ANSWER

See explanation

EXPLANATION

The standard form of a quadratic equation is:

$y = a {x}^{2} + bx + c$

To convert this function to standard form, you follow the steps below:

• Factor 'a' from the variable terms
• Add and subtract the square of half the coefficient of x.
• Factor the perfect squares
• Simplify the constant terms to get the vertex form as
• $y = a {(x - h)}^{2} + k$

For example:

Given the standard form:

$y = 2 {x}^{2} + 12x + 10$

Factor 2 from the variable terms

$y = 2 {(x}^{2} + 6x) + 10$

Add and subtract the square of 3.

$y = 2 {(x}^{2} + 6x + 9 - 9) + 10$

$y = 2 {(x}^{2} + 6x + 9) + 2( - 9) + 10$

Factor the perfect square an simplify

$y = 2 ({x + 3)}^{2} - 8$

This is the vertex form