Questions: Graph this function: y=3x-9+2

Solution Steps

The vertex of the absolute value function $y = |ax + b| + c$ is given by $x = -\frac{b}{a}$. In this case, $a = 3$ and $b = -9$, so the x-coordinate of the vertex is $x = -\frac{-9}{3} = 3$. Substituting $x = 3$ into the equation, we get $y = |3(3) - 9| + 2 = |9 - 9| + 2 = 0 + 2 = 2$. So the vertex is $(3, 2)$.

Choose a value for x, say $x=0$. Substituting this into the equation gives $y = |3(0) - 9| + 2 = |-9| + 2 = 9 + 2 = 11$. So, another point on the graph is $(0, 11)$.

Choose another value for x, say $x=6$. Substituting this into the equation gives $y = |3(6) - 9| + 2 = |18 - 9| + 2 = |9| + 2 = 9 + 2 = 11$. So, a third point on the graph is $(6, 11)$.

Final Answer