Question

Need help on number 20

Answer 1

The vertex is (-2, -1)
Here are points:
(-4,3)
(-3,0)
(-2,-1)
(-1,0)
(0,3)

Answer 2

• vertex: (-2, -1)
• axis of symmetry: x = -2
• graph: see below

Explanation:

The equation is in vertex form ...

y = a(x -h)² +k . . . . . . . . vertex (h, k) and vertical scale factor "a"

y = (x +2)² -1

so, you can read the vertex coordinates directly from the equation:

(h, k) = (-2, -1)

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The line of symmetry is the vertical line through the vertex, so has equation ...

x = h

x = -2 . . . . for this parabola

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The vertex is always a point on the graph.

At x-values ±1 either side of the vertex, the vertical distance from the vertex is "a". Here, that is 1 unit, so the points (-3, 0) and (-1, 0) are on the graph.

At x-values ±2 either side of the vertex, the vertical distance from the vertex is a·2². Here that is 4 units, so the points (-4, 3) and (0, 3) are on the graph.

This is basically what the vertex form of the equation is telling you.