Question

How do you find the vertex and axis of symmetry, and then graph the parabola given by: `y= -3x^2 + 5`?

Answer 1

Axis of symmetry is `x=0` .
Vertex is `(0,5)`
The graph will be a downward opening parabola.

Explanation:

`y=-3x^x+5` is a quadratic equation in the form `ax^2+bx+c`, where `a=-3, b=0, c=5`.

Axis of Symmetry

The axis of symmetry is determined using the formula `x=(-b)/(2a)`.

`x=(0)/(2*-3)=(0)/-6=0`

The axis of symmetry is `x=0`.

Vertex

The vertex is the maximum or minimum point on the parabola. In this case, since the coefficient of `x^2` is `-3`, the parabola will open downward and the vertex will be the maximum point.

The `x` value of the vertex is `0` from the axis of symmetry.

To find the value of `y` for the vertex, substitute `0` for `x` in the equation and solve for `y`.

`y=-3x^2(0)+5=`

`y=0+5=5`

The vertex is `(0,5)`.

Determine several points on both sides of the axis of symmetry.

`x=-2`, `y=-7`
`x=-1`, `y=2`
`x=0`, `y=5` (vertex)
`x=1`, `y=2`
`x=2,` `y=-7`

Plot the points on a graph and sketch a curved parabola through the points. Do not connect the dots.

graph{y=-3x^2+5 [-16.02, 16, -8.01, 8.01]}