Quadratic Inequalities and Functions

This video tutorial explains how to solve a quadratic inequality both by hand and graphically. It begins with an introduction to the problem, followed by a detailed step-by-step solution using factorization and interval testing. The tutorial then demonstrates how to solve the inequality graphically by analyzing the function's graph and identifying intervals where the function is above the x-axis. The video concludes with a comparison of the two methods, highlighting the efficiency of graphical solutions when x-intercepts are real and rational.

What is the first step in solving a quadratic inequality by hand?

• Test values in each interval

• Graph the function

• Use interval notation

• Determine the x-values where the equation equals zero

Which of the following is a factor of the quadratic equation 'two x squared plus three x minus five'?

• x + 5

• x - 2

• 2x - 5

• 2x + 5

What is the x-value when 'x minus one' equals zero?

• x = 0

• x = 1

• x = -1

• x = 2

Why are open points used on the number line for the values where the equation equals zero?

• Because zero is greater than zero

• Because zero is not greater than zero

• Because zero is equal to zero

• Because zero is less than zero

Which test value is used for the interval to the left of negative five halves?

• x = 0

• x = 2

• x = -2

• x = -3

What is the result when x equals zero in the inequality?

• True, part of the solution

• False, not part of the solution

• True, but not part of the solution

• False, but part of the solution

How is the solution expressed using interval notation?

• From zero to infinity

• From negative infinity to negative five halves and from one to infinity

• From negative five halves to one

• From negative infinity to positive infinity

What does the graph of the function represent in terms of the inequality?

• The function is equal to the x-axis

• The function is tangent to the x-axis

• The function is below the x-axis

• The function is above the x-axis

When is the function above the x-axis on the right side?

• When x is less than one

• When x is greater than one

• When x is equal to one

• When x is less than negative five halves

What is a key advantage of solving the inequality graphically?

• It is only useful for irrational x-intercepts

• It is straightforward if x-intercepts are real and rational

• It is more complex

• It requires more calculations