# The vertex form of the equation of a parabola is y + 10 = 3(x-1)^2 what is the standard form of the equation?

Dec 5, 2016

y= $3 {x}^{2} - 6 x - 7$

#### Explanation:

Simplify the given equation as

$y + 10 = 3 \left({x}^{2} - 2 x + 1\right)$
Therefore y= $3 {x}^{2} - 6 x + 3 - 10$

Or, y= $3 {x}^{2} - 6 x - 7$, which is the required standard form.

Dec 5, 2016

$y = 3 {x}^{2} - 6 x - 7$

Please see the explanation for the steps.

#### Explanation:

Expand the square using the pattern ${\left(a - b\right)}^{2} = {a}^{2} - 2 a b + {b}^{2}$

$y + 10 = 3 \left({x}^{2} - 2 x + 1\right)$

Distribute 3 through the ()s:

$y + 10 = 3 {x}^{2} - 6 x + 3$

Subtract 10 from both sides:

$y = 3 {x}^{2} - 6 x - 7$

This is standard form.