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:

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:

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:

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`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.

`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`

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` |

## No comments:

## Post a Comment