Graph the following functions in Desmos (press enter to add a new function)
y = x2 - 2x - 8
y = x2 - 2x - 3
y = x2 + 2x - 15
y = x2 - 2x - 15
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6 points
6
Question 2
2.
Match the characteristics to the functions. Each function should have an intercept form equation, solutions, y-intercept, axis of symmetry, vertex, and range.
y-intercept: (0, -15)
Vertex: (1, -9)
Axis of Symmetry: x = 1
Solutions: x = 3, x = -1
Range: y ≥ -16
y = (x - 3)(x + 5)
y = (x - 3)(x + 1)
Vertex: (1, -16)
y = (x - 4)(x + 2)
Vertex: (-1, -16)
y = (x + 3)(x - 5)
Solutions: x = -3, x = 5
Range: y ≥ -4
Solutions: x = 3, x = -5
Vertex: (1, -4)
Range: y ≥ -9
y-intercept: (0, -3)
Solutions: x = 4, x = -2
Axis of Symmetry: x = -1
y-intercept: (0, -8)
y = x2 - 2x - 8
y = x2 - 2x - 3
y = x2 + 2x - 15
y = x2 - 2x - 15
1 point
1
Question 3
3.
Sort the functions according to their end behaviors
y = (x + 3)(x - 4)
y = -x2
y = -10x2 + 7x - 8
y = x2
y = 2x2 -4x + 12
y = -3x2 + 6x - 9
y = -(x + 3)(x - 4)
y = 2.6x2 + 9x - 4
as x → ∞, f(x) → ∞;
as x → -∞, f(x) → ∞
as x → ∞, f(x) → -∞;
as x → -∞, f(x) → -∞
2 points
2
Question 4
4.
Match the graphs with their negative regions
Draggable item
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Corresponding Item
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(-1, 3)
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(-∞, -1) and (3, ∞)
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(-3, 1)
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(-∞, -3) and (1, ∞)
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(-2, 4)
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(-∞, -2) and (4, ∞)
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(-4, 2)
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(-∞, -4) and (2, ∞)
1 point
1
Question 5
5.
What is the average rate of change over the interval 0 ≤ x ≤ 2?
1 point
1
Question 6
6.
What is the average rate of change over the interval [-4, -1]?
1 point
1
Question 7
7.
What is the average rate of change over the interval [-2, -1]?
0 points
0
Question 8
8.
What happens to the average rate of change as it gets closer to the vertex?