Find the standard equation of a parabola with vertex at 9 6

Find the standard equation of a parabola with vertex at (9, 6) passing through the point (12, 5). Remember to write your answers as exact numbers (fractions), rather than a decimal approximation. y = (x)^2

Solution

Solution

Given a vertex (9,6) and a point (12,5) on a parabola,
First, we recall a function f(x)=a(x-h)²+k, which will give us vertex (h,k).

So the function we are looking for should look like f(x)=a(x-9)²-6,

and since the parabola passes through (12,5),

we have 5=a(12-9)²-6,

which means

a = (11/9) and

y = (11/9)(x-9)²-6.