# What is the standard form of y=5(x-3)^2+3?

Nov 17, 2015

Standard form $\to a {x}^{2} + b x + c$
If you meant to ask: 'What is this equation when presented in standard form'? Then you have $\to y = 5 {x}^{2} - 6 x + 12$

#### Explanation:

The standard form is $y = a {x}^{2} + b x + c$

However, if you wish to present this equation in standard form we have:

$y = 5 \left({x}^{2} - 6 x + 9\right) + 3$
$y = 5 {x}^{2} - 6 x + 12$

Nov 17, 2015

5x^2−30x+48

#### Explanation:

• Expand ${\left(x - 3\right)}^{2}$ in the equation:

5(x−3)(x-3)+3

• Distribute the 5 to the first parenthesis:

5(x-3
= (5 * x)+(5*-3)
$= 5 x - 15$

So now you have 5x−15(x-3)+3.

• Now distribute the $5 x$ & $- 15$ to the next parenthesis:

5x−15(x-3)
= (5x*x)+(5x*-3)+(-15*x)+(-$15 \cdot$-3)
$= 5 {x}^{2} - 15 x - 15 x + 45$
$= 5 {x}^{2} - 30 x + 45$

So now you have $5 {x}^{2} - 30 x + 45 + 3$.

• Finally, add the constant (+3):

$45 + 3 = 48$

$5 {x}^{2} - 30 x + 48$