Answer:
a) The vertex will be at (-2, -1), and the parabola will look like a smiley face. 5 points on the parabola would be: (3, 24), (-3, 0), (2, 15), (-1, 0) and (1, 8).
b) The focus will be at (-2, 0), the directrix will be at y = -2, and the axis of symmetry will be at x = -2.
Step-by-step explanation:
a) The vertex (-2, -1) can be found by first setting the parentheses (x+2) equal to zero and solving to get the x value -2, then setting x equal to zero and solving to get the y value of -1.
The parabola will be pointing up on both ends because the equation for it is positive (given 1 multiplied by parentheses) and it has a degree of 2.
The xy table to find the points would look like this:
x | y
3 | 24
-3 | 0
2 | 15
-1 | 0
1 | 8
b) The focus is one unit above the vertex, so the y value increases by 1. The directrix is a line 1 unit below the vertex, so its y value is 1 less than the vertex's. The axis of symmetry is the same as the x value of the vertex with infinite y values.
