Graphing quadratic equations in the vertex form

If the quadratic is given in the vertex form, it is very easy to find out the coordinates of the vertex form the equation/function.

As a rule, for the quadratic in the vertex form `y = a(x - h)^2 + k` the coordinates of the vertex are given by `(h, k)`

For example, for the quadratic function:

`f(x) = 2(x - 3)^2 - 8`

the coordinates of the vertex are (3, -8)

After obtaining the coordinates of the vertex from the given quadratic equation/function, we need to get the x-intercepts of the parabola. In order to obtain the x-intercepts of the quadratic, solve the quadratic for f(x) = 0, that is, we will solve the equation:

`2(x - 3)^2 - 8 = 0`
`2(x - 3)^2 = 8`
`(x - 3)^2 = 4`
`x - 3 = sqrt(4)`
`x - 3 = 2 or x - 3 = -2`
`x = 5 or x = 1`

Therefore the x-intercepts of the above equation are (5, 0) and (1, 0). If x-intercepts of a parabola don't exist, or if the x-intercept coincides with the vertex, then you need to find one or more points on either side of the axis of symmetry.

Now plot the vertex and the x-intercepts of the given quadratic and join them by a freehand curve in order to obtain the parabola. For the quadratic `2(x - 3)^2 - 8`, the graph is as follows:

Graph of `y = 2(x - 3)^2 - 8`