### Home > CALC > Chapter 1 > Lesson 1.4.3 > Problem 1-170

1-170.

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

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

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

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