9-3A Solving Quadratic Equations by Finding

Square Roots.

Algebra 1 Glencoe McGraw-Hill Linda

Stamper

You must learn how to use a calculator! There

are many makes and models. Read the instruction

booklet.

Enter a problem into the calculator for which you

already know the answer. For example

v

4

2

2

2nd

v

4

Keystrokes for TI-30X IIS

Keystrokes for TI-30X A

Evaluate the expression. Give the exact value,

if possible. Otherwise, approximate to the

nearest hundredth. You may use a calculator

for this section.

Example 1

What is the positive square root of 8?

Example 2

What is the negative square root of 11?

Example 3

What is the positive and negative square root of

27?

hundredths

Inverse Operations

Recall the use of inverse operations to solve

equations.

What is the inverse operation of addition? What

is the inverse operation of subtraction? What is

the inverse operation of multiplication? What is

the inverse operation of division? What is the

inverse operation of a square number?

The inverse of a square number is a square root.

A quadratic equation is an equation that can be

written in the standard form

Quadratic equations can have one solution, two

solutions or no real solutions.

If b 0, the equation becomes

One way to solve a quadratic equation of this

form is to isolate the x2 on one side of the

equation. Then find the square root(s) of each

side.

Remember Squaring a number and finding the

square root(s) of a number are inverse operations.

Solve the equation. Write the solutions as

integers if possible. Otherwise, round to the

nearest tenth.

How can you tell this is a quadratic equation?

Isolate the square term.

Undo the square by using square root.

Evaluate the radicals.

Do not give this answer!

One of the equations is not solved for a positive

variable! An equation is not considered solved

if the variable is negative. What do you get

when you undo the negative variable?

Solve the equation. Write the solutions as

integers if possible. Otherwise, round to the

nearest tenth.

Isolate the square term.

Undo the square by using square root.

Evaluate the radicals.

Remember the variable cannot have a sign

because a negative variable is not solved.

Solve the equations. Write the solutions as

integers if possible. Otherwise, round to the

nearest tenth.

Example 4

Example 5

Example 6

Remember the variable cannot have a sign

because a negative variable is not solved.

Solve the equations. Write the solutions as

integers if possible. Otherwise, round to the

nearest tenth.

Example 7

Example 8

Example 9

Example 10

Solve the equations. Write the solutions as

integers if possible. Otherwise, round to the

nearest tenth.

Example 7

Example 8

Solve the equations. Write the solutions as

integers if possible. Otherwise, round to the

nearest tenth.

Example 9

Example 10

no real solution

Remember the variable cannot have a sign

because a negative variable is not solved.

Solve the equations. Write the solutions as

integers if possible. Otherwise, round to the

nearest tenth. Remember a sign indicates two

solutions (roots).

Factor the P.S.T.

There are two solutions (roots)

Solve the equations. Write the solutions as

integers if possible. Otherwise, round to the

nearest tenth.

Example 11

Example 13

Example 12

Example 16

Example 15

Example 14

Hint Isolate the squared term on one side of

the equal sign.

Solve the equations. Write the solutions as

integers if possible. Otherwise, round to the

nearest tenth.

Example 11

Example 12

Solve the equations. Write the solutions as

integers if possible. Otherwise, round to the

nearest tenth.

Example 14

Example 13

Solve the equations. Write the solutions as

integers if possible. Otherwise, round to the

nearest tenth.

Example 16

Example 15

Homework

9-A5 Handout A5.