Finding the Vertex and Maximum or Minimum of a Parabola
To find the vertex of a parabola you just need the following formula:
Once you calculate a value for x, use that value in the formula of the
parabola to calculate the corresponding value for y. That point (x, y) is the
vertex of the parabola.
Example: Find the vertex of the parabola y = x2 + 6x + 8
Step 1: Identify a, b, and c.
a = 1; b = 6; c = 8
Step 2:
Step 3: Find y when x = - 3.
y = (- 3)2 + 6(- 3) + 8
y = 9 – 18 + 8 = - 9 + 8 = - 1
Step 4: The vertex is (- 3, - 1)
Maxima and Minima
Every parabola that has an x2 either opens upwards or downwards. You can
tell which way it opens by the sign on a. If a is positive, it opens upward; if
a is negative it opens downward.
If a parabola opens upward, the
vertex is the lowest point on the
graph and the y-coordinate of the
vertex is the minimum.
If a parabola opens downward, the
vertex is the highest point on the
graph and the y-coordinate of the
vertex is the maximum.