A parabola with its vertex at (25,18) and its axis of symmetry parallel to the y-axis passes through point (0,43). Write an equation of the parabola. Then find the value of y when x=40

Question

A parabola with its vertex at (25,18) and its axis of symmetry parallel to the y-axis passes through point (0,43). Write an equation of the parabola. Then find the value of y when x=40

Answer 1

Because it is given that the axis of symmetry is parallel to the y-axis it means that the parabola opens up or down. The standard form for a parabola that opens up/down is

y = a(x-h)² + k

where (h,k) is the vertex. The vertex is given as (25,18), which means that

h = 25 and k = 18. We are also given that the parabola goes through the point (0,43). We can use these values of x, y, h and k in the formula to determine the value of a:

y = a(x-h)² + k

43 = a(0-25)² + 18

43 - 18 = 625a

25 = 625a

a = 25/625

a = 1/25

Therefore, the equation for this parabola is

y = (1/25)(x-25)² + 18

The value of y when x = 40 would be found by

y = (1/25)(40 - 25)² + 18

y = (1/25)(15)² + 18

y = (1/25)(225) + 18

y = 9 + 18

y = 27

Hope this helps!