Question

Determine whether this is a parabola: y = 9x² + 36x +38

If it is a parabola, write the equation in standard form:
(y – k)² = 4p(x – h) or (x – h)² = 4p(y – k).
Otherwise, leave the rest blank.
h
k
p

Answer 1

Explanation:

`y=9x^2+36x+38\\=9(x^2+4x)+38\\=9(x^2+2*2x+2^2)+38-9*4\\=9(x+2)^2+2\\\\(x+2)^2=(y-2)/(9) \\\\h=-2\\k=2\\4p=(1)/(9) \ \Longrightarrow\ p=(1)/(36)`