Question 1
The function f(x) = 2x² + 12x + 5 can also be written as f(x) = 2(x + 3)² − 13. Which feature of the graph of f is revealed most directly by the second form?
Show answer & explanation
Correct answer: D - The minimum value of the function
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The 5162 exam has 60 questions and runs 2 hours 30 minutes.
These 10 free 5162 questions are organized by exam domain, so you can see how each part of the Praxis Algebra I (5162) blueprint is tested. Reveal the answer and explanation under each question.
The function f(x) = 2x² + 12x + 5 can also be written as f(x) = 2(x + 3)² − 13. Which feature of the graph of f is revealed most directly by the second form?
Correct answer: D - The minimum value of the function
A model rocket's height, in meters, is given by h(t) = −4.9t² + 29t + 1.5, where t is the number of seconds after launch. Solving h(t) = 0 gives t ≈ −0.05 and t ≈ 5.97. Which statement correctly interprets these solutions?
Correct answer: D - Only t ≈ 5.97 is viable, because a negative time has no meaning in this context.
To solve x² = 7x, a student divides both sides by x and concludes that x = 7. Which statement best describes the student's work?
Correct answer: A - It lost the solution x = 0, since dividing by x assumes x ≠ 0.
If ax − 7 = bx + 2 and a ≠ b, which expression is equal to x?
Correct answer: C - x = 9/(a − b)
The equation 2x² + kx + 8 = 0 has exactly one real solution. What are all the possible values of k?
Correct answer: B - k = 8 and k = −8
Which statement about the system 3x + 2y = 12 and 6x + 4y = 9 is true?
Correct answer: C - It has no solution, because the lines have the same slope but different y-intercepts.
What is the average rate of change of f(x) = x² − 3x over the interval from x = 1 to x = 5?
Correct answer: B - 3
A charity is buying identical gift baskets that cost $18 each and has a budget of $500. The total cost is modeled by C(n) = 18n, where n is the number of baskets. What is the most appropriate domain for C in this context?
Correct answer: D - All integers n such that 0 ≤ n ≤ 27
The function f is defined by f(x) = 3x − 2 for x < 5 and f(x) = x² − 10 for x ≥ 5. What is the value of f(5)?
Correct answer: B - 15
A sequence is defined by a(1) = 5 and a(n) = 2 · a(n − 1) for n > 1. Which explicit formula generates the same sequence?
Correct answer: A - a(n) = 5 · 2^(n − 1)
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