Quadratic and Linear Function Concepts

This video is a comprehensive review for a semester final exam, covering various mathematical topics. It begins with an introduction and overview, followed by sections on graphing using intercepts, solving absolute value equations, and transformations of functions. The video also covers solving and graphing inequalities, exponent problems, and completing the square. Further, it delves into quadratic equations, imaginary numbers, and graphing quadratic inequalities. The video concludes with a discussion on transformations and vertex form, providing a thorough preparation for the exam.

What is the first step in graphing a linear equation using intercepts?

• Identify the x-intercept by setting y to zero.

• Find the slope of the line.

• Calculate the midpoint of the line.

• Plot the y-intercept on the graph.

How do you solve an absolute value equation like |3x - 1| = 11?

• Multiply both sides by 3.

• Square both sides of the equation.

• Set 3x - 1 equal to 11 and -11.

• Add 11 to both sides.

What transformation occurs when a quadratic function is shifted up 7 units?

• The graph is compressed vertically.

• The graph is shifted up 7 units.

• The graph is shifted left 7 units.

• The graph is reflected over the x-axis.

When solving the inequality 8x - 2 - 10x - 30 ≤ 10, what is the next step after combining like terms?

• Divide by -2 and flip the inequality sign.

• Add 32 to both sides.

• Multiply both sides by 2.

• Subtract 10 from both sides.

In a system of inequalities, what does a dashed line indicate?

• The inequality is greater than or equal to.

• The inequality is strict (not equal to).

• The inequality includes the line.

• The line is not part of the solution.

How do you simplify an expression with a negative exponent?

• Flip the base to the reciprocal and change the exponent to positive.

• Subtract the exponent from the base.

• Add the exponent to the base.

• Multiply the base by the exponent.

What is the first step in completing the square for the equation 2x^2 + 12x = -5?

• Add 5 to both sides.

• Divide all terms by 2.

• Subtract 12x from both sides.

• Multiply all terms by 2.

What is the axis of symmetry for the quadratic equation y = 2x^2 + 4x + 15?

• x = 2

• x = -1

• x = 1

• x = -2

Which of the following is a solution to the quadratic equation using the quadratic formula?

• x = 2 ± √26/2

• x = -2 ± √26/2

• x = 1 ± √26/2

• x = -1 ± √26/2

What does a positive discriminant indicate about the solutions of a quadratic equation?

• There are two complex solutions.

• There are two real solutions.

• There is one real solution.

• There are no real solutions.