# How do you find the axis of symmetry, and the maximum or minimum value of the function y= 2x^2 + 12x-11?

Jan 30, 2016

Axis of symmetry$\text{ "-> x=-3" }$

Minimum$\text{ } \to \left(x , y\right) \to \left(- 3 , - 29\right)$

#### Explanation:

The $2 {x}^{2}$ is positive so the general shape of the graph is similar to that of the letter U. Thus we have a minimum

Write as;$\text{ } y = 2 \left({x}^{2} + 6 x\right) - 11$

Consider the $+ 6 \text{ from "6x" }$in the brackets

Multiply this by negative half:

$\left(- \frac{1}{2}\right) \times 6 = - 3$

This turns out to be ${x}_{\text{vertex}} = - 3$

So the $\textcolor{b l u e}{\text{axis of symmetry is at } x = - 3}$, which is line parallel to the y-axis but passes through $x = - 3$
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This is also the x-value for the minimum

So by substituting it back into the original equation we find the corresponding value for y

color(blue)(y_("minimum")=2(-3)^2+12(-3)-11" "=" "-29)