Question

How do you find the axis of symmetry, and the maximum or minimum value of the function `y = −3x^2 − 12x + 5`?

Answer 1

The axis of symmetry is `x=-2`.
The vertex is `(-2,17)`.

Explanation:

`y=-3x^2-12x+5` is in standard form, `ax^2+bx+c`, where `a=-3, b=-12, and c=5"`.

The axis of symmetry is an imaginary vertical line that separates the parabola into two equal halves. The formula for the axis of symmetry is `x=(-b)/(2a)`.

`x=(-(-12))/(2*-3)=`

`x=12/(-6)=`

`x=-2`

This is also the `x` value of the vertex, which is the maximum point of this parabola. We can know that the vertex is the maximum point because when `a<0`, the parabola opens downward.

To find the `y` value for the vertex, substitute `-2` for `x` in the equation and solve for `y`.

`y=-3x^2-12x+5`

`y=-3(-2)^2-12(-2)+5=`

`y=-3(4)+24+5=`

`y=-12+24+5=`

`y=17`

The vertex is `(-2,17)`.

graph{y=-3x^2-12x+5 [-9.64, 10.36, 7.694, 17.69]}