Quadratic Functions and Their Properties

This video tutorial covers free response practice for a second semester final exam. It begins with graphing systems of equations to find intersection points, followed by solving a quadratic word problem using both the quadratic formula and factoring. The tutorial then explains how to find the vertex and intercepts of a quadratic function. Finally, it includes sketching the graph of the quadratic function and analyzing its domain, range, and maximum height.

What is the intersection point of the two lines graphed in the first question?

• (2, 5)

• (0, 7)

• (3, -1)

• (1, 3)

In the quadratic word problem, what is the value of 'a' in the equation?

• 18

• 3

• 15

• -3

Using the quadratic formula, what are the two solutions for t?

• 2 and 4

• 1 and -6

• 0 and 5

• -1 and 6

When factoring the quadratic equation, what are the two numbers that multiply to -6 and add to -5?

• 3 and -2

• 2 and -3

• -6 and 1

• 5 and -1

What are the x-intercepts of the quadratic function?

• (3, 0) and (4, 0)

• (-1, 0) and (6, 0)

• (0, 18) and (2.5, 36.75)

• (1, 0) and (5, 0)

What is the x-coordinate of the vertex of the quadratic function?

• 2.5

• 0

• 6

• 3

What is the y-intercept of the quadratic function?

• (0, 0)

• (0, 18)

• (2.5, 36.75)

• (6, 0)

At what time does the box reach its maximum height?

• 2.5 seconds

• 6 seconds

• 3 seconds

• 0 seconds

What is the maximum height reached by the box?

• 0 feet

• 36.75 feet

• 6 feet

• 18 feet

What is the range of the quadratic function in the context of the problem?

• 0 to 18

• 0 to 2.5

• 0 to 6

• 0 to 36.75