Solving Quadratic Systems Concepts

The video tutorial explains how to solve systems of equations involving quadratics. It begins with an introduction to systems of equations and the concept of finding intersection points of graphs. The tutorial outlines a four-step process for solving these systems, which includes rewriting equations, using methods like factoring or completing the square, and verifying solutions. Two examples are provided: one using factoring and another using completing the square, demonstrating the application of these methods to find solutions.

What is a system of equations in the context of quadratics?

• A single linear equation

• A set of equations involving one or more graphs

• A set of equations involving only linear terms

• A single quadratic equation

What is the first step in solving a system of quadratic equations?

• Checking the solutions

• Rewriting the equations in standard form

• Finding the y-values

• Graphing the equations

Which method is NOT mentioned as a way to solve for x in quadratic systems?

• Graphing

• Factoring

• Quadratic formula

• Completing the square

When factoring the quadratic equation, what is the purpose of drawing a box and a diamond?

• To graph the equation

• To check the solutions

• To organize the terms for factoring

• To find the y-values

What are the x-values found when solving the equation x^2 - 4x - 21 = 0 by factoring?

• x = 7 and x = -3

• x = 3 and x = -7

• x = 7 and x = 3

• x = -7 and x = 3

After finding the x-values, what is the next step in solving the system?

• Graphing the solutions

• Finding the y-values by substitution

• Checking the solutions

• Rewriting the equations

What is the y-value when x = 7 in the equation y = x^2 + 11?

• y = 49

• y = 60

• y = 11

• y = 7

What is the purpose of completing the square in solving quadratic systems?

• To graph the equation

• To find the y-values

• To simplify the equation

• To find the x-values

In completing the square, what is added to both sides of the equation x^2 + 4x = 5 to make it a perfect square?

• 9

• 4

• 2

• 5

What are the x-values found when solving the equation x^2 + 4x + 4 = 9 by completing the square?

• x = 2 and x = -2

• x = 3 and x = -3

• x = 1 and x = -5

• x = 5 and x = -1