# How do you find the axis of symmetry, and the maximum or minimum value of the function y = 2x^2 + 24x + 62?

Nov 12, 2017

Axis of symmetry is $x + 6 = 0$ and mimima occurs at $x = - 6$, when the value of function is $- 10$.

#### Explanation:

Let us first convert te equation to vertex form i.e. $y = a {\left(x - h\right)}^{2} + k$. The maxima or minima of such a function depends on $a$. If it is positive then we have a minima and if $a$ is negative we have a maxima.

In such a equation, $\left(h , k\right)$ is vertex and indicates that maxima / minima occurs when $x = h$ and the value of function then is $k$. Further, $x - h = 0$ is the axis of symmetry.

Now we have $y = 2 {x}^{2} + 24 x + 62$

i.e. $y = 2 \left({x}^{2} + 12 x + 31\right)$

or $y = 2 \left({x}^{2} + 12 x + 36 - 5\right)$

or $y = 2 {\left(x + 6\right)}^{2} - 10$

Hence axis of symmetry is $x + 6 = 0$ and mimima occurs at $x = - 6$, when the value of function is $- 10$.

graph{2x^2+24x+62 [-13.05, 6.95, -11.16, -1.16]}