Example 2

Determine the equation of the quadratic function represented in the graph below in vertex form, factored form, and standard form.

Step 1: Organize the information that is given.

The vertex is (3, 0).

The y-intercept = −27.

Step 2: Select a form that works with the given information. Because the vertex is known, the vertex form would be a good form to work with.

h = 3 and k = 0

Step 3: Determine the value of a.

Substitute the y-intercept (0, −27), into the equation of the function and solve for a.

Step 4: Write the equation of the quadratic function in vertex form.

Step 5: Write the equation of the quadratic function in factored form.

There is no k-value, so the equation can quickly be rewritten in factored form.

Step 6: Write the equation of the quadratic function in standard form by expanding the factored form.

Step 7: Final statement.

Vertex form:

Factored form:

Standard form:

Please refer to Page 341, Example 3, of Principles of Mathematics 11 for another example for determining the equation of a quadratic function when given a graph.