Question

How do you find the axis of symmetry, graph and find the maximum or minimum value of the function `y=-3x^2`?

Answer 1

Maximum at `(0, 0)`; axis of symmetry at `x = 0`

Explanation:

Given: `y = -3x^2`

When the equation is in `y = Ax^2 + Bx + C = 0` form:

The vertex is `(-B/(2A), f(-B/(2A)))` and

the axis of symmetry is `x = -B/(2A)`

`-B/(2A) = -0/-3 = 0`

`f(0) = -3(0^2) = 0`

Maximum is at the vertex `(0, 0)`, axis of symmetry `x = 0`

To find more points, use point plotting. Since `x` is the independent variable, select any `x` and calculate the corresponding `y`:

`ul(" "x" "|" "y" ")`
`" "-2" "|-12`
`" "-1" "|-3`
`" "1" "|-3`
`" "2" "|-12`

Graph of `y = -3x^2`:

graph{-3x^2 [-5, 5, -15, 5]}