Question

How do you identify the important parts of `y= -7x^2` to graph it?

Answer 1

The axis of symmetry is `x=0`/
The vertex is `(0,0)`.

Explanation:

`y=-7x^2` is a quadratic equation in standard form `ax^2+bx+c`, where `a=-7, b=0, and c=0`.

Axis of Symmetry: an imaginary vertical line the divides the parabola into two equal halves.

Formula for axis of symmetry: `x=(-b)/(2a)`

Since `b=0`, the axis of symmetry is `x=0`.

Vertex: The maximum or minimum point `(x,y)` of a parabola. Since the coefficient of `a` is negative, this parabola opens downward and the vertex is the maximum point. The `x` value for the vertex is the value for the axis of symmetry, where `x=0`.

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

`y=-7x^2=`

`y=-7(0)^2=0`

The vertex is `(0,0)`.

Determine a few points on both sides of the axis of symmetry.

`x=-2,` `y=-28`
`x=-1,` `y=-7`
`x=0,` `y=0` (vertex)
`x=1,` `y=-7`
`x=2,` `y=-28`

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

graph{y=-7x^2 [-14.49, 17.53, -11.08, 4.94]}