# Question f07be

Mar 15, 2017

$\left(5 , - 4\right) \text{ and } x = 5$

#### 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 and a is a constant.

$y = {\left(x - 5\right)}^{2} - 4 \text{ is in this form}$

$\text{with "h=5" and } k = - 4$

$\Rightarrow \text{vertex } = \left(5 , - 4\right)$

The parabola will have a maximum/ minimum dependent on.

• "If "a>0" then minimum " uuu

• "If "a<0" then maximum" nnn#

$\text{here "a=1>0rArr" minimum at } \left(5 , - 4\right)$

The axis of symmetry passes through the vertex and is vertical with equation x = 5

graph{(y-x^2+10x-21)(y-1000x+5000)=0 [-10, 10, -5, 5]}