ALGEBRA 2
CHAPTER # 2
TEST PREP
1. A PARABOLA HAS AN AXIS OF SYMMETRY
OF Y = -6 AND PASSES THROUGH THE
POINT (-3,5), FIND ANOTHER POINT THAT
LIES ON THE GRAPH OF THE PARABOLA.
2. LET THE GRAPH OF g BE A VERTICAL
𝟏
SHRINK BY A FACTOR OF , FOLLOWED BY
𝟒
A TRANSLATION OF 5 UNITS DOWN OF
THE GRAPH OF 𝒇 𝒙 = 𝒙𝟐 .
3. LET THE GRAPH OF g BE A TRANSLATION 3 UNITS
DOWN AND 5 UNITS TO THE RIGHT
OF THE GRAPH OF 𝒇 𝒙 = −𝟑 𝒙 + 𝟓 𝟐 − 𝟒.
WRITE A RULE FOR g.
4. IDENTIFY THE FOCUS, DIRECTRIX, AND
AXIS OF SYMMETRY OF
𝟏 𝟐
𝒙=−
𝒚
𝟑𝟔
5. EXPLAIN WHY A QUADRATIC
FUNCTION MODELS THE DATA. SHOW
WHAT YOU MEAN VISUALLY.
UNITS SOLD (X)
1
2
3
4
5
PROFIT
(THOUSANDS OF
DOLLARS)
29
60
75
84
87
6. WRITE THE EQUATION OF THE
PARABOLA
7. WRITE THE EQUATION OF THE
PARABOLA
8. WRITE THE EQUATION OF THE PARABOLA
9. WRITE THE EQUATION OF THE PARABOLA
10. IDENTIFY THE FOCUS, DIRECTRIX, AND
AXIS OF SYMMETRY OF
𝟏 𝟐
𝒇 𝒙 =− 𝒙 .
𝟖
THEN GRAPH THE EQUATION.
11. YOUR NEW COMPANY HIRES A MATHEMATICIAN
TO MODEL THE PROFITS “p” THAT YOUR COMPANY
MAKES FROM SELLING ITS PRODUCT. THE EQUATION
𝒑(𝒄) = −𝟏𝟎𝒄𝟐 + 𝟑𝟔𝟎𝒄 + 𝟐𝟎
IS THE EQUATION THE MATHEMATICIAN COMES UP
WITH WHERE “c” IS THE COST OR PRICE OF THE
PRODUCT YOUR MAKE. WHAT PRICE SHOULD YOU
PUT ON YOUR PRODUCT IF YOU WANT TO MAXIMIZE
YOUR COMPANY PROFITS?
12. GRAPH THE FOLLOWING:
a. LABEL THE VERTEX AND AXIS OF SYMMETRY
b. DESCRIBE WHERE THE FUNCTION IS
INCREASING AND DECREASING
f ( x)  ( x  4)  3
2
13. GRAPH THE FOLLOWING:
a. LABEL THE VERTEX AND AXIS OF SYMMETRY
b. DESCRIBE WHERE THE FUNCTION IS
INCREASING AND DECREASING
y  x  4x  8
2
14. AT A RECENT NEWS MAKING EVENT YOU
NOTICED THAT THE NEWS CHANNEL TRUCKS
WERE USING PARABOLIC DISHES TO BEAM THEIR
NEWS FEEDS. YOU TOOK A CROSS SECTION
THROUGH THE CENTER OF THE DISH AND
MEASURED THE DISTANCE FROM THE VERTEX OF
THE PARABOLA TO THE BROADCASTING ELEMENT TO
BE 4 FEET. WRITE AN EQUATION THAT REPRESENTS
THE CROSS SECTION OF THE DISH ASSUMING
THE VERTEX IS AT THE ORIGIN AND THE
DISH POINTS TO THE RIGHT. WHAT IF THE
DISH POINTS STRAIGHT UP?
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