Quadratic Functions Test Answer Key with Scoring – Algebra 1

Question 1 Vertex Form Features (2 points)

1. Vertex (−2, 7). Since a = −3 < 0, it opens down.
2. Axis x = −2; the vertex is the highest point, so the maximum is 7.

Scoring: 1 point per part.

Question 2 Vertex from Standard Form (2 points)

Axis x = 10 ÷ 2 = 5. y = 25 − 50 + 7 = −18. The y-intercept is the constant term, 7.

Axis x = 5; vertex (5, −18); y-intercept 7

Scoring: 1 point for axis and vertex, 1 point for the y-intercept.

Question 3 Complete the Square (2 points)

Half of 12 is 6: y = (x² + 12x + 36) − 36 + 31 = (x + 6)² − 5.

y = (x + 6)² − 5; vertex (−6, −5)

Scoring: 1 point for the vertex form, 1 point for the vertex.

Question 4 Features from a Graph (3 points)

1. Vertex (−1, 4); axis x = −1.
2. x-intercepts (−3, 0) and (1, 0); y-intercept (0, 3).
3. Domain: all real numbers. The parabola opens down with maximum 4, so the range is y ≤ 4.

Scoring: 1 point per part.

Question 5 Factored Form (2 points)

Zeros: −3 and 7. The axis is (−3 + 7) ÷ 2 = 2. At x = 2: (5)(−5) = −25.

Zeros −3 and 7; vertex (2, −25)

Scoring: 1 point for the zeros, 1 point for the vertex.

Question 6 Write an Equation (3 points)

1. y = a(x − 3)² + 1. At (5, 9): 9 = 4a + 1, so a = 2. y = 2(x − 3)² + 1
2. 2(x² − 6x + 9) + 1 = 2x² − 12x + 19

Scoring: (a) 1 point for substituting, 1 point for a and the equation. (b) 1 point.

Question 7 Thrown Ball (3 points)

1. h(0) = 48 feet.
2. t = −32 ÷ (2 · (−16)) = 1. h(1) = −16 + 32 + 48 = 64 feet at 1 second.
3. −16(t − 3)(t + 1) = 0, so t = 3 seconds (reject −1).

Scoring: 1 point per part.

Question 8 Fenced Pen (2 points)

1. A(w) = w(30 − w).
2. Zeros 0 and 30, so the vertex is at w = 15: A(15) = 15 · 15 = 225 square feet (15 ft by 15 ft).

Scoring: 1 point per part.

Question 9 Does It Cross the Axis? (1 point)

The vertex is (1, 3) and a = 2 > 0, so the minimum value is 3, above the x-axis.

No x-intercepts

Scoring: 1 point for the answer with a correct justification.