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