WGU C957 Applied Algebra Objective
Assessment 2026/2027 – Verified Q&As
with Detailed Rationales (Test Bank
Bundle - 42 Questions)
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*QUESTION 1:*
A company's profit is modeled by the function P(x) = 50x - 1000, where x is the number of units sold.
How many units must be sold to break even?
A) 20
B) 50
C) 100
D) 10
> 🎯 *CORRECT ANSWER:* A) 20
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* Break-even occurs when P(x) = 0; 50x - 1000 = 0 → x = 20.
> * *Why Distractors Fail:* Other numbers do not satisfy the equation.
> * *Core Takeaway:* Break-even is when profit = 0.
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*QUESTION 2:*
A line has a slope of 3 and passes through the point (2, 5). What is the equation of the line in slope-
intercept form?
A) y = 3x - 1
,B) y = 3x + 1
C) y = 3x - 5
D) y = 3x + 5
> 🎯 *CORRECT ANSWER:* A) y = 3x - 1
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* y - 5 = 3(x - 2) → y = 3x - 6 + 5 = 3x - 1.
> * *Why Distractors Fail:* Other options have incorrect intercepts.
> * *Core Takeaway:* Use point-slope form to find the equation.
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*QUESTION 3:*
A company's revenue is R(x) = 20x and cost is C(x) = 5x + 150. What is the break-even point?
A) 10
B) 15
C) 20
D) 30
> 🎯 *CORRECT ANSWER:* A) 10
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* Break-even when R(x) = C(x): 20x = 5x + 150 → 15x = 150 → x = 10.
> * *Why Distractors Fail:* Other numbers do not satisfy the equation.
> * *Core Takeaway:* Break-even is when revenue equals cost.
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*QUESTION 4:*
A quadratic function f(x) = x^2 - 4x + 3 has roots at:
,A) 1 and 3
B) -1 and -3
C) 1 and -3
D) -1 and 3
> 🎯 *CORRECT ANSWER:* A) 1 and 3
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* (x - 1)(x - 3) = x^2 - 4x + 3, so roots are 1 and 3.
> * *Why Distractors Fail:* Other pairs do not match.
> * *Core Takeaway:* Factor to find roots.
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*QUESTION 5:*
What is the vertex of the parabola f(x) = x^2 - 4x + 3?
A) (2, -1)
B) (2, 1)
C) (-2, -1)
D) (-2, 1)
> 🎯 *CORRECT ANSWER:* A) (2, -1)
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* x = -b/(2a) = 4/2 = 2; f(2) = 4 - 8 + 3 = -1.
> * *Why Distractors Fail:* Other points are not the vertex.
> * *Core Takeaway:* Vertex x = -b/(2a).
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*QUESTION 6:*
, A company's profit is maximized at the vertex of a quadratic function. If P(x) = -2x^2 + 20x - 30, what is
the maximum profit?
A) 20
B) 25
C) 30
D) 10
> 🎯 *CORRECT ANSWER:* A) 20
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* x = -b/(2a) = -20/(2*-2) = 5; P(5) = -2(25) + 100 - 30 = 20.
> * *Why Distractors Fail:* Other values are incorrect.
> * *Core Takeaway:* Vertex gives maximum for concave down.
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*QUESTION 7:*
What is the slope of the line through points (1, 2) and (4, 8)?
A) 2
B) 3
C) 4
D) 1/2
> 🎯 *CORRECT ANSWER:* A) 2
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* m = (8 - 2) / (4 - 1) = = 2.
> * *Why Distractors Fail:* Other values are incorrect calculations.
> * *Core Takeaway:* Slope = change in y / change in x.
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Assessment 2026/2027 – Verified Q&As
with Detailed Rationales (Test Bank
Bundle - 42 Questions)
---
*QUESTION 1:*
A company's profit is modeled by the function P(x) = 50x - 1000, where x is the number of units sold.
How many units must be sold to break even?
A) 20
B) 50
C) 100
D) 10
> 🎯 *CORRECT ANSWER:* A) 20
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* Break-even occurs when P(x) = 0; 50x - 1000 = 0 → x = 20.
> * *Why Distractors Fail:* Other numbers do not satisfy the equation.
> * *Core Takeaway:* Break-even is when profit = 0.
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*QUESTION 2:*
A line has a slope of 3 and passes through the point (2, 5). What is the equation of the line in slope-
intercept form?
A) y = 3x - 1
,B) y = 3x + 1
C) y = 3x - 5
D) y = 3x + 5
> 🎯 *CORRECT ANSWER:* A) y = 3x - 1
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* y - 5 = 3(x - 2) → y = 3x - 6 + 5 = 3x - 1.
> * *Why Distractors Fail:* Other options have incorrect intercepts.
> * *Core Takeaway:* Use point-slope form to find the equation.
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*QUESTION 3:*
A company's revenue is R(x) = 20x and cost is C(x) = 5x + 150. What is the break-even point?
A) 10
B) 15
C) 20
D) 30
> 🎯 *CORRECT ANSWER:* A) 10
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* Break-even when R(x) = C(x): 20x = 5x + 150 → 15x = 150 → x = 10.
> * *Why Distractors Fail:* Other numbers do not satisfy the equation.
> * *Core Takeaway:* Break-even is when revenue equals cost.
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*QUESTION 4:*
A quadratic function f(x) = x^2 - 4x + 3 has roots at:
,A) 1 and 3
B) -1 and -3
C) 1 and -3
D) -1 and 3
> 🎯 *CORRECT ANSWER:* A) 1 and 3
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* (x - 1)(x - 3) = x^2 - 4x + 3, so roots are 1 and 3.
> * *Why Distractors Fail:* Other pairs do not match.
> * *Core Takeaway:* Factor to find roots.
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*QUESTION 5:*
What is the vertex of the parabola f(x) = x^2 - 4x + 3?
A) (2, -1)
B) (2, 1)
C) (-2, -1)
D) (-2, 1)
> 🎯 *CORRECT ANSWER:* A) (2, -1)
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* x = -b/(2a) = 4/2 = 2; f(2) = 4 - 8 + 3 = -1.
> * *Why Distractors Fail:* Other points are not the vertex.
> * *Core Takeaway:* Vertex x = -b/(2a).
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*QUESTION 6:*
, A company's profit is maximized at the vertex of a quadratic function. If P(x) = -2x^2 + 20x - 30, what is
the maximum profit?
A) 20
B) 25
C) 30
D) 10
> 🎯 *CORRECT ANSWER:* A) 20
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* x = -b/(2a) = -20/(2*-2) = 5; P(5) = -2(25) + 100 - 30 = 20.
> * *Why Distractors Fail:* Other values are incorrect.
> * *Core Takeaway:* Vertex gives maximum for concave down.
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*QUESTION 7:*
What is the slope of the line through points (1, 2) and (4, 8)?
A) 2
B) 3
C) 4
D) 1/2
> 🎯 *CORRECT ANSWER:* A) 2
> 💡 *CLINICAL RATIONALE:*
> * *Why It's Right:* m = (8 - 2) / (4 - 1) = = 2.
> * *Why Distractors Fail:* Other values are incorrect calculations.
> * *Core Takeaway:* Slope = change in y / change in x.
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