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

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(x-h)^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, `(h,k)` 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=2x^2+24x+62`

i.e. `y=2(x^2+12x+31)`

or `y=2(x^2+12x+36-5)`

or `y=2(x+6)^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]}