Solving Quadratic Equations with Inverse Operations

The video tutorial covers quadratic equations, focusing on their graphical representation and solving methods. It introduces the inverse operations method, explaining how to solve quadratics by taking square roots and considering both positive and negative solutions. The tutorial provides examples to illustrate these concepts and discusses factoring as an alternative method for solving quadratic equations.

What are the three names given to the points where a quadratic graph crosses the x-axis?

• Intercepts, Zeros, Points

• Solutions, Intercepts, Roots

• Intercepts, Zeros, Roots

• Solutions, Zeros, Roots

When solving quadratic equations using inverse operations, when does this method work?

• When the variable is a constant

• When the variable is a fraction

• When the variable appears once and is squared

• When the variable appears twice

What happens when you take the square root of both sides of an equation involving a squared term?

• You get no solution

• You get two solutions

• You get one solution

• You get a fractional solution

In the equation x^2 = 49, what are the solutions for x?

• x = 0

• x = 7 and x = -7

• x = -7

• x = 7

What is the first step in solving the equation 4x^2 = 8?

• Multiply both sides by 4

• Add 4 to both sides

• Divide both sides by 4

• Subtract 4 from both sides

When solving the equation 3x^2 = 75, what is the value of x after taking the square root of both sides?

• x = 0

• x = 5 and x = -5

• x = -5

• x = 5

In the equation (x + 3)^2 = 25, what are the two possible values for x?

• x = 2 and x = -8

• x = 5 and x = -5

• x = 3 and x = -3

• x = 8 and x = -2

What should you do first when solving the equation (x - 2)^2 = 25?

• Take the square root of both sides

• Divide both sides by 4

• Subtract 2 from both sides

• Add 2 to both sides

Why can't inverse operations be used to solve the equation x^2 - 8x + 16 = 0?

• Because the equation has no solutions

• Because the equation is not set to zero

• Because the variable is not squared

• Because the variable appears more than once

What is the correct factorization of the equation x^2 - 8x + 16 = 0?

• (x - 4)(x - 4)

• (x - 4)(x + 4)

• (x + 4)(x + 4)

• (x - 8)(x + 2)