Unit 11: Quadratic Functions · AI-F.IF.7, AI-F.IF.8, AI-A.SSE.3
Algebra I Regents
Notes
What each form shouts. Standard: y-intercept c, and axis x = −b/(2a). Vertex: vertex (h, k) and stretch a. Factored: x-intercepts r and s. The axis of symmetry is midway between the roots.
Direction. If a > 0 the parabola opens up (minimum). If a < 0 it opens down (maximum).
Vocabulary
vertex: The turning point of a parabola; a maximum or a minimum.
axis of symmetry: The vertical line through the vertex that splits the parabola into mirror images.
roots: The x-intercepts of the graph; solutions of f(x) = 0.
Practice (no calculator unless marked)
The students in Mrs. Smith’s algebra class were asked to describe the graph of g(x) = 2(x − 3)² compared to the graph of f(x) = x². Which student response is correct?
A. Ashley said that the graph of g(x) is wider and shifted left 3 units.
B. Beth said that the graph of g(x) is narrower and shifted left 3 units.
C. Carl said that the graph of g(x) is wider and shifted right 3 units.
D. Don said that the graph of g(x) is narrower and shifted right 3 units.
A ball was launched into the air, and its height above the ground was recorded each second:
Time (sec): 0, 1, 2, 3, 4
Height (ft): 11, 59, 75, 59, 11
Based on these data, which statement is a valid conclusion?
A. The ball lands on the ground at 4 seconds.
B. The ball reaches a maximum height of 11 feet.
C. The ball was launched from a height of 0 feet.
D. The ball reaches its maximum height at 2 seconds.
The students in Mrs. Smith’s algebra class were asked to describe the graph of g(x) = 2(x − 3)² compared to the graph of f(x) = x². Which student response is correct?
A. Ashley said that the graph of g(x) is wider and shifted left 3 units.
B. Beth said that the graph of g(x) is narrower and shifted left 3 units.
C. Carl said that the graph of g(x) is wider and shifted right 3 units.
D. Don said that the graph of g(x) is narrower and shifted right 3 units.
A ball was launched into the air, and its height above the ground was recorded each second:
Time (sec): 0, 1, 2, 3, 4
Height (ft): 11, 59, 75, 59, 11
Based on these data, which statement is a valid conclusion?
A. The ball lands on the ground at 4 seconds.
B. The ball reaches a maximum height of 11 feet.
C. The ball was launched from a height of 0 feet.
D. The ball reaches its maximum height at 2 seconds.
The students in Mrs. Smith’s algebra class were asked to describe the graph of g(x) = 2(x − 3)² compared to the graph of f(x) = x². Which student response is correct?
A. Ashley said that the graph of g(x) is wider and shifted left 3 units.
B. Beth said that the graph of g(x) is narrower and shifted left 3 units.
C. Carl said that the graph of g(x) is wider and shifted right 3 units.
D. Don said that the graph of g(x) is narrower and shifted right 3 units.
A ball was launched into the air, and its height above the ground was recorded each second:
Time (sec): 0, 1, 2, 3, 4
Height (ft): 11, 59, 75, 59, 11
Based on these data, which statement is a valid conclusion?
A. The ball lands on the ground at 4 seconds.
B. The ball reaches a maximum height of 11 feet.
C. The ball was launched from a height of 0 feet.
D. The ball reaches its maximum height at 2 seconds.
The students in Mrs. Smith’s algebra class were asked to describe the graph of g(x) = 2(x − 3)² compared to the graph of f(x) = x². Which student response is correct?
A. Ashley said that the graph of g(x) is wider and shifted left 3 units.
B. Beth said that the graph of g(x) is narrower and shifted left 3 units.
C. Carl said that the graph of g(x) is wider and shifted right 3 units.
D. Don said that the graph of g(x) is narrower and shifted right 3 units.
A ball was launched into the air, and its height above the ground was recorded each second:
Time (sec): 0, 1, 2, 3, 4
Height (ft): 11, 59, 75, 59, 11
Based on these data, which statement is a valid conclusion?
A. The ball lands on the ground at 4 seconds.
B. The ball reaches a maximum height of 11 feet.
C. The ball was launched from a height of 0 feet.
D. The ball reaches its maximum height at 2 seconds.