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

Equation for the axis of symmetry is $x = - 6$. Vertex (minimum) has coordinates $\left(- 6 , - 10\right)$
Formula for the x-coordinate of the vertex of a quadratic function in standard form $\left(a {x}^{2} + b x + c = y\right)$ is $- \frac{b}{2 a}$. Substituting gives $x = - 6$. This is also the equation of the axis of symmetry, the vertical line running through the vertex. Substitute this x-value into the original equation to find the y-value of the vertex ( $y = - 10$). This gives the coordinates of the vertex of $\left(- 6 , - 10\right)$. Since a is positive, the parabola opens up, so the vertex is a minimum.