Solving Quadratics Using Square Roots

The video tutorial covers solving quadratic equations using the square root method, focusing on equations in vertex form. It provides multiple examples, including cases with perfect squares and irrational roots, demonstrating step-by-step solutions. The tutorial emphasizes the importance of inverse operations and handling both positive and negative roots, offering practice problems for viewers to try.

What is the vertex form of a quadratic equation?

• x - h^2 + k = y or 0

• ax^2 + bx + c

• x^2 + bx + c = 0

• x - h^2 + k

What is the first step in solving a quadratic equation using the square root method?

• Square both sides

• Isolate the variable

• Add or subtract constants

• Take the square root of both sides

What do you get after taking the square root of both sides of the equation?

• A single value for x

• Two values for x

• An irrational number

• A perfect square

What type of solutions might you get when solving quadratic equations?

• Both positive and negative

• Only negative

• Only positive

• Imaginary

How do you verify the solutions of a quadratic equation?

• By completing the square

• By graphing

• By factoring

• By substitution

What indicates an equation might have an irrational solution?

• A prime number under the square root

• A negative number under the square root

• A non-perfect square under the square root

• A perfect square under the square root

How can you simplify the square root of 12?

• Square root of 6

• 2 root 3

• 4 root 3

• 3 root 4

What is the correct way to express an irrational solution?

• As a whole number

• As a fraction

• As a decimal

• In simplest radical form

Why can't you add the 2 and 3 in the expression 2 + 3 root 2?

• Because they are like terms

• Because they are not like terms

• Because it would simplify to 5 root 2

• Because it's already in simplest form

What is the result of adding 2 to both sides of the equation x - 2 squared = 18?

• x = 2 - 3 root 2

• x = 2 + 3 root 2

• x = 20

• x = 18