Quadratic Functions and Inequalities

This video tutorial covers quadratic inequalities, starting with an introduction to the concept and the graph of a quadratic function. It explains how to determine where the function is positive or negative by finding the x-intercepts. The video outlines steps to solve quadratic inequalities, including finding zeros, testing intervals, and graphing solutions. Three examples are provided: a factorable inequality, one with open intervals, and a special case with no real solutions. The tutorial emphasizes using a graphing calculator for efficiency and concludes with verifying solutions graphically.

What do the x-intercepts of a quadratic function represent?

• Where the function is positive

• Where the function is negative

• Where the function equals zero

• Where the function is undefined

What is the first step in solving a quadratic inequality?

• Plotting the graph

• Using a graphing calculator

• Finding the zeros of the polynomial

• Testing interval values

When plotting on a number line, how do you decide between open and closed points?

• Based on the degree of the polynomial

• Based on the inequality symbol

• Based on the number of zeros

• Based on the graph's shape

In the first example problem, what are the test values chosen for the intervals?

• -1, 1, 10

• -4, 2, 7

• -2, 0, 8

• -3, 0, 9

What does a true test value indicate about an interval?

• The interval is false

• The interval is zero

• The interval is true

• The interval is undefined

In the second example, what is the solution set for the quadratic inequality?

• From 3/2 to 4

• From 0 to 5

• From -2 to 8

• From negative infinity to 3/2 and from 4 to positive infinity

How is the solution verified graphically in the second example?

• By checking if the graph intersects the y-axis

• By checking if the graph is above the x-axis

• By checking if the graph is a straight line

• By checking if the graph is below the x-axis

In the special case example, what is the result when there are no real zeros?

• The solution is zero

• The solution is undefined

• The entire number line is true

• The entire number line is false

What does it mean graphically when a quadratic function is always above the x-axis?

• The function is undefined

• The function is always positive

• The function is always zero

• The function is always negative

What is the interval notation for a function that is always positive?

• From negative infinity to zero

• From zero to positive infinity

• From negative infinity to positive infinity

• From zero to one