A parabola with its vertex at (20,8)​ and its axis of symmetry parallel to the y-axis passes through point (25,28)​ . Write an equation of the parabola. Then find the value of y​ when x=40​ .

Answer 1

y = a(x - 20)² + 8. To find a we use point (25,28): 28 = a(25 - 20)² + 8; 20 = 25a; a = 0.8

y = 0.8(x - 20)² + 8

If x = 40 y = 0.8(40 - 20)² + 8 = 328

Answer 2

Since the axis of symmetry is parallel to the y-axis, an equation of the parabola is y-k = a(x-h)², where

(h,k) is the vertex.

So, we have y-8 = a(x-20)².

Since the point (25,28) is on the graph, 28-8 = a(25-20)². Therefore, a = 4/5.

So, y-8 = (4/5)(x-20)²