Practice!

Sample Problem

The triangular arch of a tower lies on a coordinate grid. The lower left corner of the triangle is on the coordinate (-4,0) and the lower right corner of the triangle is on the coordinate (4,0). The top corner of the triangle has the coordinate (0,8). Assuming that the top corner is the vertex, what is the absolute value equation that connects the vertex to the bottom left and right corners?

Solution

Given the vertex (0,8), we know that our equation has to be in the form y = a|x| + 8. Plugging in (-4,0):

0 = a|-4| + 8

0 = 4a + 8

-4a = 8

a = -2

y = -2|x| + 8