Question

sketch a parabola. find the vertex, axis of sym, and the x and y intercepts y=x^2+6x+8

Answer 1

The intercepts can be solved by letting y=0 and solve x^2 + 6x +8. this is easily factored. Getting (x+4)(x+2) or intercepts at (-4,0) and (-2,0). this should be helpful when you sketch the parabola.

Answer 2

You can find the vertex by completeing the square.

Answer 3

Yes it does open upward as you show it, because the squared term is positive.

Answer 4

When you complete the square, you should get f(x)=(x+3)^2 -1. From this the vertex is
(-3, -1)