Precalculus Practice Test 9.19.3 - South Minneapolis High School Page 3
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9Precalculus Practice Test 9.1-9.3
6. Find the vertex and focus of the parabola below.
2
y
+ 6 + 8 + 20 0
y
x
We must first get the equation into standard form. We do this by grouping the x’s and y’s
together and completing the square.
6y 8x 20 0
2
y
6y
8x 20
2
y
6y 9
8x 20 9
2
y
y 3
8x 11
2
y 3
2
8 x
11
(Notice the sign change when factoring out - 8).
8
y k
2
4 p x h
This is the standard equation for a parabola that opens to the left
.
11
Matching terms, we see that the vertex is
,3
.
8
4p is equal to ‐8, meaning that p is equal to ‐2. Thus, the focus of the parabola is 2 units to
the left of the vertex, at the point
2,3
11
8
11
16
.
,3
8
8
27
,3
8
Page 3
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