Question

Graphing quadratics in vertex form - I can do the graphing part, I just can’t do the equation

Answer 1

The vertex form of the quadratic equation is y = 3 (x - 2)² - 22

How to write the equation in vertex form

The quadratic equation is written in vertex form by completing the square

This is done as follows

y = 3x² - 12x - 10

y = 3(x² - 4x) - 10

Take half of the coefficient of x, square it, and add it to both parts of the equation. In this case, the coefficient of the linear term is -4, so we have:

y = 3(x² - 4x + 4) - 10 - 3(4)

This x² - 4x + 4 can be factorized to (x - 2)²

y = 3(x² - 2x - 2x + 4) - 10 - 3(4)

y = 3(x(x - 2) - 2(x - 2)) - 10 - 12

y = 3((x - 2) (x - 2)) - 22

y = 3 (x - 2)² - 22