Key Features of Graphs Test Answer Key with Scoring – Algebra 1

Question 1 Intercepts from an equation (2 points)

y = 0: 3x = 30 so x = 10. x = 0: −5y = 30 so y = −6.

(10, 0) and (0, −6)

Scoring: 1 point per intercept.

Question 2 Features of a graph (3 points)

(a) Increasing for −6 < x < −3 and 1 < x < 5.

(b) Decreasing for −3 < x < 1.

(c) Relative maximum (−3, 4), relative minimum (1, −2).

Scoring: 1 point per part.

Question 3 Rate of change from a table (3 points)

(a) (77 − 11) ÷ (9 − 3) = 66 ÷ 6 = 11.

(b) On average, f(x) increases by 11 for each 1-unit increase in x between 3 and 9 (it is not constant: the rate between 0 and 3 is only 2).

11

Scoring: (a) 1 point for the setup, 1 for 11; (b) 1 point.

Question 4 Zeros and end behavior (2 points)

(a) −x² + 9 = 0 gives x² = 9, so x = 3 or x = −3.

(b) The parabola opens down, so f(x) → −∞ as x → ∞ and as x → −∞.

Zeros ±3; falls at both ends

Scoring: 1 point per part.

Question 5 Drone flight (3 points)

(a) (100 − 20) ÷ 4 = 20 ft/s.

(b) (40 − 100) ÷ 6 = −10 ft/s.

(c) The negative sign means the drone is descending on average between 4 and 10 seconds.

20 ft/s and −10 ft/s

Scoring: 1 point per part.

Question 6 Axis of symmetry (2 points)

(a) The vertex is at x = −2, so the line is x = −2.

(b) (1, 4) is 3 right of the line, so the mirror point is 3 left: (−5, 4). Check: f(−5) = 9 − 5 = 4.

x = −2; (−5, 4)

Scoring: 1 point per part.

Question 7 Compare two functions (2 points)

f has rate 6 and g increases by 7 each step, so g has the greater rate.

f(0) = −4 and g(0) = 2, so g also has the greater y-intercept.

g in both cases

Scoring: 1 point for each comparison.

Question 8 Parabola features (3 points)

(a) The vertex is (2, −4), a minimum.

(b) The graph crosses the x-axis at 0 and 4.

(c) The graph is below the x-axis for 0 < x < 4.

(2, −4) minimum; 0 and 4; negative for 0 < x < 4

Scoring: 1 point per part.