Question

An architect uses a computer program to design a skateboard ramp. The function f(x) = ax^2 represents the shape of the ramp's cross section. A portion of the design is shown. On the ramp, a person can skateboard from point A through point B and over to point C. If point C is the same distance above the x-axis as point B, what are its coordinates? Explain. Assume that each grid line represents one unit, with the intersection of the x- and y-axes being the point (0,0). Fill in the blanks: Since point B is located at ______ and the skateboard ramp is symmetric above the _____ , point C will be located at ______.

Answer 1

From inspection of the graph, point B is at (7, 2).

The vertex of the parabola is at (0, 0) so the axis of symmetry is x = 0.

Therefore, point C will have the same y-value as point B, and the same x-value but in the negative ⇒ (-7, 2).

Final answers

B = (7, 2)

origin (0, 0)

C = (-7, 2)