Understanding Quadratic Functions

The video tutorial explains how to analyze a quadratic function's graph by identifying its domain, range, intervals of increase and decrease, vertex, axis of symmetry, minimum value, and intercepts. The domain is all real numbers, and the range starts from the vertex's y-value. The function decreases to the vertex and increases thereafter. The vertex is the lowest point, and the intercepts are where the graph crosses the axes.

What is the domain of a quadratic function?

• All real numbers

• All positive numbers

• All negative numbers

• Only integers

How can the domain of a quadratic function be expressed using interval notation?

• [0, 1]

• [0, ∞)

• (-∞, ∞)

• (-∞, 0]

What is the range of a quadratic function with a vertex at y = -4?

• [0, ∞)

• (-∞, ∞)

• [-4, ∞)

• (-∞, -4]

In which interval is the quadratic function decreasing?

• (-∞, ∞)

• (-∞, -3)

• [0, ∞)

• (-3, ∞)

At what x-value does the function start increasing?

• 3

• 0

• -3

• -5

What is the x-coordinate of the vertex of the parabola?

• 0

• -3

• -5

• 3

What is the y-coordinate of the vertex of the parabola?

• -4

• 0

• 5

• 4

What is the equation of the axis of symmetry for the parabola?

• x = 3

• x = -5

• x = -3

• x = 0

Where does the parabola cross the x-axis?

• (5, 0)

• (0, 5)

• (-5, 0) and (-1, 0)

• (-3, -4)

What is the y-intercept of the quadratic function?

• (0, -5)

• (0, 5)

• (5, 0)

• (-5, 0)