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Characteristics of Quadratic Functions

Last updated almost 4 years ago

8 questions

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6

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2

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Question 1

1.

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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Question 2

2.

Question 3

3.

Sort the functions according to their end behaviors

y = -x2
y = -(x + 3)(x - 4)
y = -3x2 + 6x - 9

Question 4

4.

Draggable item		Corresponding Item

Question 5

5.

What is the average rate of change over the interval 0 ≤ x ≤ 2?

Question 6

6.

What is the average rate of change over the interval [-4, -1]?

Question 7

7.

What is the average rate of change over the interval [-2, -1]?

Question 8

8.

What happens to the average rate of change as it gets closer to the vertex?

Match the characteristics to the functions. Each function should have an intercept form equation, solutions, y-intercept, axis of symmetry, vertex, and range.

Vertex: (1, -4)

y-intercept: (0, -15)

Solutions: x = 3, x = -5

Solutions: x = -3, x = 5

y = (x - 3)(x + 1)

Solutions: x = 3, x = -1

Vertex: (1, -9)

Vertex: (1, -16)

y = (x - 3)(x + 5)

Vertex: (-1, -16)

Range: y ≥ -16

y = (x - 4)(x + 2)

Axis of Symmetry: x = 1

Solutions: x = 4, x = -2

y-intercept: (0, -8)

y-intercept: (0, -3)

Range: y ≥ -4

y = (x + 3)(x - 5)

Axis of Symmetry: x = -1

Range: y ≥ -9

y = x2 - 2x - 8

y = x2 - 2x - 3

y = x2 + 2x - 15

y = x2 - 2x - 15

y = 2x2 -4x + 12

y = 2.6x2 + 9x - 4

y = (x + 3)(x - 4)

y = x2

y = -10x2 + 7x - 8

as x → ∞, f(x) → ∞;
as x → -∞, f(x) → ∞

as x → ∞, f(x) → -∞;
as x → -∞, f(x) → -∞

Match the graphs with their negative regions

(-1, 3)

(-∞, -1) and (3, ∞)

(-3, 1)

(-∞, -3) and (1, ∞)

(-2, 4)

(-∞, -2) and (4, ∞)

(-4, 2)

(-∞, -4) and (2, ∞)