CCSS.HSA.F.IF.Q.1.A1.DD.0 - How to find the vertex of the absolute value function y = |9x -3|

Sangeetha Pulapaka (last edited 4 years ago) (Expert, Educator @Qalaxia)

STEP 1: Recall what are absolute values

STEP 2: Recall what is an absolute value function

STEP 3: Find the vertex of the absolute value function

Recall what is the vertex of a function

To find the x-value of the function y = |9x - 3|, set the equation to zero

9x - 3 = 0

9x - 3 + 3 = 0 + 3

9x = 3

x = \frac{3}{9}

x = \frac{1}{3}

Replace the variable x with \frac{1}{3} in the expression

y = | 9 \frac{1}{3} - 3|

y = |3 -3| = 0

The absolute value vertex is (\frac{1}{3},0)