Find the formula for a quadratic function that passes through the points (3,1) and (1,25) and has as its axis of symmetry x=33.

Question

Find the formula for a quadratic function that passes through the points (3,1) and (1,25)

and has as its axis of symmetry x=33.

Answer 1

the quadratic function is f(x) = ax^2 + bx + c

axis of symmetry at x=33.

x = -b/2a = 33

-b = 66a

b = -66a

(3,1): 1 = 9a + 3b + c

(1,25) 25 = a+ b + c

subtracting them:

-24 = 8a + 2b

-12 = 4a + b

-12 = 4a + -66a

-12 = -62 a

a = 12/62 = 6/31

b = -66(6/31) = -396/31

per the original first equation 1 = 9 * (6/31) + (-396/31)(3) + c

1 = 54/31 - 1188/31 + c

1 = -1134/31 + c

1 + 1131/31 = c

1165/31 = c

(6/31) x^2 - 396/31 x + 1165/31 = f(x)

(1/31) (6x^2 - 396x + 1165) = f(x)

I ran it through desmos, it it checks. So do the two given points.