Tutoring math 11 – which is needed for nursing, among other careers – you’ll need to explain how to identify the vertex of a quadratic function.
Vertex form is designed to easily yield the vertex of a quadratic function. A quadratic function of the form
y=a(x-p) ² + q
has vertex at (p,q).
Example 1: Find the vertex of y=-3(x-4)² +9
Solution: the vertex is at (4,9).
Notice the (“opposite, same”) pattern: the x-coordinate is opposite to what you see in the brackets, whereas the y-coordinate is the same as what you see added (or subtracted) at the end.
Example 2: Find the vertex of y=2(x+5)² -3
Solution: the vertex is at (-5,-3).
Notice that the number multiplying in front of the brackets does not affect the vertex.
Example 3: Find the vertex of y=(x-5)²
Solution: Remembering the form y=a(x-p)² +q, we need to discern the values of p and q. Clearly, p=5. q=0, because
can also be written as
y=(x-5)² + 0.
Therefore, the vertex is at (5,0).
Example 4: Find the vertex of y=3x² + 7
Solution: Going back to y=a(x-p) ² + q, we realize that although q=7, we seem to be missing p. However, we can rewrite our equation as y=3(x-0)² + 7. Now, we realize that p=0. The vertex is at (0,7).
Identifying the vertex can be tricky, but I hope this helps.
Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC