Question

How do you graph `y=1/4x^2`?

Answer 1

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

Explanation:

`y=1/4x^2` is the standard form for a quadratic equation `y=ax^2+bx+c`, where `a=1/4, b=0, and c=0`.

The graph of a quadratic equation is a parabola. Since #a>0, the parabola opens upward. In order to graph the parabola, we need to determine the the axis of symmetry and the vertex. Then determine some additional points.

The axis of symmetry is the line `x=(-b)/(2a)=(0)/(2xx1/4)=0`.
`x=0` and is also the `x` value of the vertex. The axis of symmetry where `x=0` is superimposed on the y-axis.

To determine the `y` value of the vertex, substitute `0` for `x` in the equation.

`y=1/4*0^2=0`

The vertex is `(0,0)`.

Now determine some other on the parabola by substituting values for `x` that are on both sides of the axis of symmetry.

`y=1/4x^2`

`x=-6,` #y=9 #x=-4,``y=4# #x=-2,``y=1# #x=0,``y=0# (vertex) #x=2,``y=1# #x=4,``y=4# #x=6,``y=9#

Plot the vertex and the other points. Sketch a parabola through the points, keeping in mind that the graph is a curve. Do not connect the dots.

graph{y=1/4x^2 [-10, 10, -1.63, 8.37]}