We learn how to find the equation of a parabola by writing it in vertex form

In the previous section, we learnt how to write a parabola in its vertex form and saw that a parabola’s equation: \[y = ax^2+bx+c\] could be re-written in vertex form: \[y = a\begin{pmatrix}x – h \end{pmatrix}^2+k\] where:

We can use the vertex form to find a parabola’s equation. The idea is to use the coordinates of its vertex (maximum point, or minimum point) to write its equation in the form \(y=a\begin{pmatrix}x-h\end{pmatrix}^2+k\) (assuming we can read the coordinates \(\begin{pmatrix}h,k\end{pmatrix}\) from the graph) and then to find the value of the coefficient \(a\).

This is explained in the step-by-stem mathod, below, as well as in the tutorials.

Given the graph of a parabola for which we’re given, or can clearly see:

This two-step method is better/further explained in the following tutorial, take the time to watch it now.

In the following tutorial we learn how to find a parabola’s using the coordinates of its vertex as well as the coordinates of its \(y\)-intercept.

Using the two-step method we’ve just learned, find the equation of each of the following parabola in the following two forms:

Note: this exercise can be downloaded as a worksheet to practice with worksheet

In the following tutorial we learn how to find a parabola’s using the coordinates of its vertex as well as the coordinates of another point along its length (that isn’t the \(y\)-intercept).

For each of the parabola shown here:

Note: this exercise can be downloaded as a worksheet to practice with: worksheet