Name: ______Date:______Period:______
GSE Algebra I Unit 3 Practice Test
Constructed Response.
Name: ______Date:______Period:______
1.A catapult launches a boulder with an upward velocity of 132 ft/s. The height of the boulder, h, in feet after t seconds is given by the function . A. Rewrite the function in vertex form.
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B. Use the vertex to determine how long does it take the boulder to reach its maximum height. ______
C. Use the vertex to determine the boulder’s maximum height. ______
2.What are the roots of the function whose graph is shown?
3.What is the factored form of the expression ?
4.Find the zeros of the function by factoring.
5.Solve the quadratic equation using any method.
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6.The function models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff. How long will it take the stone to hit the ground? Round to the nearest hundredth of a second.
7.
A. Describe the transformation of f(x) from the graph of
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B. Determine the interval (x values) for where the function is increasing
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C. Determine the intervals (x values) for where the function is decreasing
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8.Identify the vertex and the axis of symmetry of the graph of the function .
9.Find the solutions to the equation.
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10.What is the vertex form of the equation?
11.Explain the translation from the graph of to .
12.Factor. 9x2 + 18x + 8
13.Find the minimum or maximum value of . Then state the domain and range of the function.
14. Find the average rate of change of the function below between the intervals [-3, 0]
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15.Use the Quadratic Formula to find the solutions to the equation.
Name: ______Date:______Period:______
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Name: ______Date:______Period:______
1.You live near a bridge that goes over a river. The underneath side of the bridge is an arch that can be modeled with the function where x and y are in feet. How high above the river is the bridge (the top of the arch)? How long is the section of bridge above the arch?
A / The bridge is about 1592.26 ft. above the river and the length of the bridge above the arch is about 796.13 ft.B / The bridge is about 278.25 ft. above the river and the length of the bridge above the arch is about 1592.26 ft.
C / The bridge is about 1592.26 ft. above the river and the length of the bridge above the arch is about 278.25 ft.
D / The bridge is about 278.25 ft. above the river and the length of the bridge above the arch is about 796.13 ft.
2.What steps transform the graph of to ?
A / reflect across the x-axis, translate 2 units to the left, translate up 5 units, stretch by the factor 3B / reflect across the x-axis, translate 2 units to the right, translate down 5 units, stretch by the factor 3
C / translate 2 units to the right, translate down 5 units, stretch by the factor 3
D / translate 2 units to the left, translate up 5 units, stretch by the factor 3
3.Solve the equation.
A / –9, 9B /
C / –3, 3
D / no real number solutions
4.Find the zeros of the function.
A / , –3B / 2, 3
C / , 3
D / 2, –3
5.Find the vertex of the graph and determine if it is a minimum or maximum.
A / (1, 0); minimumB / (0, 1); maximum
C / (1, 0); maximum
D / (0, 1); minimum
6.Find the zeros of the function
A /B /
C /
D /
7.Which equation is represented by the function in the graph?
A /B /
C /
D /
8.Find f(4) for f(x) = .
A / f(4) = 113B / f(4) = 79
C / f(4) = 23
D / f(4) = –17
9.Which of the following is a factor. x2 + 12x + 36 ?
A / (x + 12)B / (x + 1)
C / (x + 36)
D / (x + 6)
10.Describe the end behavior of the graph.
A / as x, f(x) and as x +, f(x)B / as x, f(x) and as x +, f(x)
C / as x, f(x) and as x +, f(x)
D / as x, f(x) and as x +, f(x)
11.Which equation correctly shows f(x) in intercept form?
A / f(x) =B / f(x) =
C / f(x) =
D / f(x) =