Parabola equation

Question

Parabola for 3,-1 that passes through 5,7

Answer 1

A parabola that opens upward or downward has equation y = a(x - h)² + k, where (h,k) is the vertex.

If the vertex is (3,-1), then we have: y = a(x - 3)² - 1

Since (5,7) is on the graph, 7 = a(5 - 3)² - 1

7 = 4a - 1

So, a = 2.

Equation: y = 2(x - 3)² - 1