Chapter 9 Algebra Worksheet With Answers - Montville Township Public Schools Page 15
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31SOLUTION:
2
2
The graph of f (x) = ax
stretches or compresses the parent graph vertically. ince a =
, the graph of y =
x
is
Study Guide and Review - Chapter 9
2
the graph of y = x
vertically compressed.
29. Write an equation for the function shown in the graph.
SOLUTION:
Since the graph is a parabola that has only been translated vertically and stretched vertically, the equation must have
2
+ c. The y-intercept of the graph is –3, so c = –3. The graph contains the point (1, –1). Use this
the form y = ax
point to find the value of a.
2
Write a quadratic equation using a = 2 and c = –3. So, an equation for the function shown in the graph is y = 2x
– 3.
2
30. PHYSICS A ball is dropped off a cliff that is 100 feet high. The function h = −16t
+ 100 models the height h of the
2
ball after t seconds. Compare the graph of this function to the graph of h = t
.
SOLUTION:
2
Because the leading coefficient is negative, the graph opens downward. The function can be written f (t) = at
+ c,
2
2
where a = –16 and c = 100. Since 100 > 0 and
> 1, the graph of h = −16t
+ 100 is the graph of y = x
vertically stretched and shifted up 100 units from the parent function.
Solve each equation by completing the square. Round to the nearest tenth if necessary.
2
31. x
+ 6x + 9 = 16
SOLUTION:
The solutions are 1 and –7.
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Page 15
2
32. −a
− 10a + 25 = 25
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