Question

If the quadratic function f(x) = 3x² + 12x - 5, is expressed in the form
f(x) = 3(x-p)² + q, where p and q are constants, find the value of p and of q.

Answer:​

Answer 1

f(x) = 3(x-p)² + q,

f(x) = 3(x² - 2px + p²)+ q,

f(x) = 3x² - 6px + 3p²+ q,

but f(x) = 3x² + 12x - 5, (given)

so, by comparing them,we get

-6p = 12 and 3p²+ q = - 5

solving them,

we get p = - 2 and q = - 17