Characteristics of Quadratic Functions

Last updated over 3 years ago
8 questions
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

6

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

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

Match the graphs with their negative regions

Draggable itemCorresponding Item
(-1, 3)
(-∞, -1) and (3, ∞)
(-3, 1)
(-∞, -3) and (1, ∞)
(-2, 4)
(-∞, -2) and (4, ∞)
(-4, 2)
(-∞, -4) and (2, ∞)
1

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

1

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

1

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

0

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