Vertex Form: 𝑦 = 𝑎(𝑥 − 𝒽)2 + 𝑘

  • 𝑎: determines whether the parabola opens up or down and how steep the curve is

  • 𝒽: x-coordinate of the vertex

  • 𝑘: y-coordinate of the vertex

Match each definition below to the graph it describes.

𝑓(𝑥) = - 0.5(𝑥 - 3)2 + 2

1

A

a parabola that opens down, passing through the points (0,-1) (2,3) and (5,-1).

𝑔(𝑥) = 2(𝑥 + 1)2 - 4

2

B

a parabola that opens down, with roots at 1 and 5 and a vertex at (3,2).

𝒽(𝑥) = - (𝑥 - 2)2 + 3

3

C

a parabola that opens up, passing through the points (0,5) (4,1) and (8,5).

𝑗(𝑥) = 0.25(𝑥 - 5)2 - 4

4

D

a parabola that opens up, with roots at 1 and 9 and a vertex at (5, -4).

$$\displaystyle k(x) = \frac{1}{4}(x - 4)^2 + 1)$$

5

E

a parabola that opens up, passing through (-3,4) (-1,-4) and (1, 4).

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