Understanding Quadratic Functions

This video tutorial covers the key components of quadratic functions, including determining the orientation of the parabola, calculating the axis of symmetry, finding the vertex coordinates, and identifying the x and y intercepts. It also explains how to graph the function, determine the domain and range, and identify 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 position of the vertex

• The value of the x-intercept

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

• By setting the derivative to zero

• Using the formula y = ax^2 + bx + c

• Using the formula x = -b/2a

• By finding the midpoint of the intercepts

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

• 3

• 5/4

• 0

• -1/2

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

• x = 0 and x = 3

• x = -1/2 and x = 3

• x = 1/2 and x = -3

• x = 0 and x = -1/2

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

• (3, 0)

• (0, 3)

• (0, -3)

• (3, 3)

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

• (1.25, 6.125)

• (0, 3)

• (3, 0)

• (-1/2, 0)

What is the domain of any quadratic function?

• All integers

• All real numbers

• All negative numbers

• All positive numbers

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

• y ≤ 6.125

• y ≥ 6.125

• y ≥ 0

• y ≤ 0

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

• From -1/2 to 3

• From 0 to 3

• From negative infinity to 5/4

• From 5/4 to positive infinity

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

• From 0 to 3

• From negative infinity to 5/4

• From -1/2 to 3

• From 5/4 to positive infinity