# What is the vertex of y=4(x + 2)^2 + 3?

Nov 29, 2015

Vertex$\to \left(x , y\right) \to \left(- 2 , 3\right)$

#### Explanation:

Consider the $\textcolor{b l u e}{2}$ in $\left(x + \textcolor{b l u e}{2}\right)$

${x}_{\text{vertex}} = \left(- 1\right) \times \textcolor{b l u e}{2} = \textcolor{red}{- 2}$

Now that you now the value for $x$ all you need to do is substitute it back into the original formula to obtain the value of y

So ${y}_{\text{vertex}} = 4 {\left(\left(\textcolor{red}{- 2}\right) + 2\right)}^{2} + 3$

${y}_{\text{vertex}} = 3$
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The equation form of $y = 4 {\left(x + 2\right)}^{2} + 3$ is also known as completing the square. It is derived from the standard quadratic form of
$y = a {x}^{2} + b x + c$

For this question its standard quadratic form is:
$y = 4 \left({x}^{2} + 4 x + 4\right) + 3$
$y = 4 {x}^{2} + 16 x + 19$
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