How do you find the axis of symmetry, and the maximum or minimum value of the function y = 6x^2 + 24x + 16?

Jul 17, 2017

$x + 2 = 0$ is axis of symmetry and minimum value of $y = 6 {x}^{2} + 24 x + 16$ is $- 8$ at $x = - 2$.

Explanation:

$y = 6 {x}^{2} + 24 x + 16$

$= 6 \left({x}^{2} + 4 x + 4\right) - 24 + 16$

$= 6 {\left(x + 2\right)}^{2} - 8$

As $6 {\left(x + 2\right)}^{2}$ has minimum value $0$ when $x = - 2$

Minimum value of $y = 6 {x}^{2} + 24 x + 16$ is $- 8$.

Further when $x = - 2 \pm k$, $y = 6 {k}^{2} - 8$

hence $y = 6 {x}^{2} + 24 x + 16$ is symmetric around $x = - 2$ and

$x = - 2$ or $x + 2 = 0$ is axis of symmetry.

graph{(6x^2+24x+16-y)(x+2)=0 [-4, 0, -10, 10]}