Question

HELP ME

Drag the labels to the correct locations on the table. Not all tiles will be used.
Match each attribute of a parabola to the correct quadratic function.

Answer 1

1. C, E, G

2. A, D, H

Explanation:

Compare each equation to the form ...

f(x) = 1/(4p)(x -h)^2 +k

In this form, p is the distance from the vertex to the focus (positive is up), and (h, k) is the location of the vertex. The focus is (h, k+p); the directrix is y=k-p.

1. The equation tells us ...

(h, k) = (1, 4)

1/(4p) = (-1) . . . ⇒ . . . p = -1/4

So, we have ...

• vertex: (1, 4) . . . . . . . . (G)
• focus: (1, 3 3/4) . . . . . (C)
• directrix: y=4 1/4 . . . . (E)

--

2. The equation tells us ...

(h, k) = (-1, 4)

1/(4p) = 2 . . . ⇒ . . . p = 1/8

So, we have ...

• vertex: (-1, 4) . . . . . . . . (A)
• focus: (-1, 4 1/8) . . . . . . (H)
• directrix: y = 3 7/8 . . . (D)