# The equation f(x)= 4x^2- 16x +9 represents a parabola. What is the vertex of the parabola?

Jan 2, 2017

$\text{vertex at } \left(2 , - 7\right)$

#### Explanation:

The equation of a parabola in $\textcolor{b l u e}{\text{vertex form}}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where (h ,k) are the coordinates of the vertex.

$\text{Rearranging " f(x)=4x^2-16x+9" into this form}$

$f \left(x\right) = 4 \left({x}^{2} - 4 x + \frac{9}{4}\right)$

$= 4 \left[{\left(x - 2\right)}^{2} \textcolor{red}{- 4} + \frac{9}{4}\right]$

$= 4 \left[{\left(x - 2\right)}^{2} - \frac{7}{4}\right]$

$\Rightarrow f \left(x\right) = 4 {\left(x - 2\right)}^{2} - 7 \leftarrow \text{ in vertex form}$

$\text{here " h=2" and } k = - 7$

$\Rightarrow \text{vertex } = \left(2 , - 7\right)$
graph{4x^2-16x+9 [-20, 20, -10, 10]}