Question

Where is the vertex of the parabola?
y = x2 + 2x – 3

a. above the x-axis
b. below the x-axis
c. on the x-axis
d. on the y-axis

Answer 1

complete the square and decide.
f(x)=a(x-h)^2+k
if k=0, vertex is on the x-axis, k>0 it is above
if h=0, vertex is on the y-axis, h<0 it is to the right.

Answer 2

I tried to do that, I can't figure it out

Answer 3

I can give an example:
For \(x^2+4x-3\)
\(x^2+4x-3\)
=\(x^2+2(2x)+4-4-3\)
=\((x^2+2(2x)+4)-7\) notice the perfect square on the left!
=\((x+2)^2-7\)
compare with f(x)=a(x-h)^2+k
so a=1, h=-2, k=-7
so the vertex (of this example) is to the left of the y-axis, and below the x-axis.

Answer 4

thank you! I understand a lot better now!

Answer 5

You're welcome! :)