Quadratic Functions and Their Graphs

The video tutorial explains how to graph quadratic functions and determine their domain and range using interval notation. It covers two examples: f(x) = x^2 - 2 and g(x) = -2x^2 + 4. For each function, a table of values is used to plot points on a coordinate plane, and the domain and range are analyzed. The domain for both functions is all real numbers, while the range is determined by the vertex of the parabola. The video emphasizes the use of interval notation to express these concepts.

What is the parent function of f(x) = x^2 - 2?

• f(x) = x^2

• f(x) = x^2 + 2

• f(x) = x^2 - 4

• f(x) = x^2 + 4

What is the value of f(1) for the function f(x) = x^2 - 2?

• 0

• -2

• 1

• -1

Which of the following points is on the graph of f(x) = x^2 - 2?

• (0, 0)

• (2, 0)

• (0, -2)

• (1, 1)

What is the domain of the function f(x) = x^2 - 2?

• x > 0

• All real numbers

• x ≤ 0

• x ≥ 0

What is the range of the function f(x) = x^2 - 2?

• y ≥ -2

• y ≤ -2

• y < -2

• y > -2

What is the vertex of the function g(x) = -2x^2 + 4?

• (-2, 0)

• (2, 0)

• (0, -4)

• (0, 4)

What is the value of g(2) for the function g(x) = -2x^2 + 4?

• 2

• 4

• 0

• -4

Which of the following points is on the graph of g(x) = -2x^2 + 4?

• (2, 4)

• (0, 4)

• (1, 2)

• (0, 0)

What is the domain of the function g(x) = -2x^2 + 4?

• All real numbers

• x ≤ 0

• x ≥ 0

• x > 0

What is the range of the function g(x) = -2x^2 + 4?

• y > 4

• y < 4

• y ≥ 4

• y ≤ 4