Item 12 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

An equation is __ ?

When  x=40, y=__?

Answer 1

If the vertex is (24,18) and has a y value of 18, then the axis of symmetry is y=18

Its an upward opening parabola if it has y value > 18, 43>18.

(0,43) is a point on the parabola such that

43 = a(18)^2 + 25

a(18)^2 = 43-25 = 18

a = 18/18^2 = 1/18

the equation is

y- 18 = (1/18)(x-25)^2

or

y = (1/18)(x^2 - 50x + 625) + 18

y = x^2/18 - 25x/9 + 625/18 + 18

y = x^2/18 -25x/9 + 949/18

when x = 40

y= (1/18)(40-25)^2 + 18 = (1/18)(225) + 18 = (25/2)+ 18 = 30.5

y= 30.5 when x = 40

Answer 2

f(x) = a(x - 25)² + 18

f(0) = 43

43 = a(43 - 25)² + 18

Can you solve for a and answer?