Question

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

Answer 1

Equation for the axis of symmetry is `x=-6`. Vertex (minimum) has coordinates `(-6, -10)`

Explanation:

Formula for the x-coordinate of the vertex of a quadratic function in standard form `(ax^2 + bx+c = y)` is `-b/(2a)`. 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 `(-6, -10)`. Since a is positive, the parabola opens up, so the vertex is a minimum.