Quadratic Functions and Their Properties

This video tutorial explains how to analyze a quadratic function graphically. It covers finding the y-intercept, identifying the turning point, and determining the roots of the function. The example used is the quadratic function y = x^2 + 4x - 12. The y-intercept is found at -12, the turning point is at (-2, -16), and the roots are at x = -6 and x = 2. The video emphasizes understanding these concepts through graphical representation and provides step-by-step instructions for each part.

What is the general form of a quadratic function?

• y = ax^2 + bx + c

• y = mx + c

• y = a/x + b

• y = ax^3 + bx^2 + cx + d

In the quadratic function y = x^2 + 4x - 12, what is the coefficient of x?

• 0

• 4

• -12

• 1

Where does the y-intercept occur on a graph?

• At the lowest point of the graph

• At the highest point of the graph

• Where the graph crosses the y-axis

• Where the graph crosses the x-axis

What is the y-intercept of the function y = x^2 + 4x - 12?

• 12

• 4

• 0

• -12

What is the y-coordinate of the point where the function y = x^2 + 4x - 12 crosses the y-axis?

• 0

• -12

• 2

• -6

What is the significance of the y-intercept in a quadratic function?

• It is the lowest point on the graph

• It is the highest point on the graph

• It is the point where the graph crosses the y-axis

• It is the point where the graph crosses the x-axis

What is a turning point on a graph?

• Where the graph is horizontal

• Where the graph changes direction

• Where the graph crosses the y-axis

• Where the graph crosses the x-axis

What are the coordinates of the turning point for the function y = x^2 + 4x - 12?

• (-2, -16)

• (0, -12)

• (2, 0)

• (-6, 0)

What does a positive gradient indicate about the direction of a curve?

• The curve is vertical

• The curve is horizontal

• The curve is going up

• The curve is going down

What does a negative gradient indicate about the direction of a curve?

• The curve is vertical

• The curve is going down

• The curve is going up

• The curve is horizontal