CPM Homework Help : CALC Problem 1-170

Use a parabola and absolute value function to find a piecewise defined function that will produce the graph shown below:

Hint 1:

Vertex form of a parabola: $y = a(x − h)^² + k$ , where $(h, k)$ is the vertex. Absolute value: $y = a|x − h| + k$

Hint 2:

Solve for $a$ by evaluating both equations at $(2,7)$ .

Hint 3:

Because the function for this graph is piecewise, there is an $x$ -coordinate / boundary point where each function ceases to defined.