Quadratic Functions and Their Properties

This video tutorial covers the key components of quadratic functions, including how to determine the orientation of a parabola, find the axis of symmetry, calculate the vertex coordinates, and identify the x and y intercepts. It also explains how to graph the function and determine its domain and range. Finally, the video discusses the intervals where the function is increasing or decreasing.

What determines whether a parabola opens upwards or downwards?

• The value of the constant term

• The sign of the leading coefficient

• The axis of symmetry

• The value of the vertex

How do you calculate the axis of symmetry for a quadratic function?

• Using the formula x = -b/2a

• Using the formula y = ax^2 + bx + c

• By finding the midpoint of the intercepts

• By setting the derivative to zero

What is the x-coordinate of the vertex for the function f(x) = -2x^2 + 5x + 3?

• 3

• 0

• -1/2

• 5/4

What are the x-intercepts of the function f(x) = -2x^2 + 5x + 3?

• (-1/2, 0) and (3, 0)

• (0, 3) and (3, 0)

• (1, 0) and (2, 0)

• (-3, 0) and (1/2, 0)

What is the y-intercept of the function f(x) = -2x^2 + 5x + 3?

• (0, 3)

• (3, 0)

• (5, 0)

• (0, -3)

Which point is the vertex of the function f(x) = -2x^2 + 5x + 3?

• (-1/2, 0)

• (1.25, 6.125)

• (0, 3)

• (3, 0)

What is the domain of any quadratic function?

• Numbers between -1 and 1

• All real numbers

• Only positive numbers

• Only negative numbers

What is the range of the function f(x) = -2x^2 + 5x + 3?

• y ≥ 3

• y ≤ 6.125

• y ≥ 6.125

• y ≤ 3

On which interval is the function f(x) = -2x^2 + 5x + 3 increasing?

• (-∞, 1.25)

• (1.25, ∞)

• (-∞, 0)

• (0, ∞)

On which interval is the function f(x) = -2x^2 + 5x + 3 decreasing?

• (-∞, 0)

• (0, 1.25)

• (-∞, 1.25)

• (1.25, ∞)