9-3A Solving Quadratic Equations by Finding Square Roots.

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9-3A Solving Quadratic Equations by Finding Square Roots. Algebra 1 Glencoe McGraw-Hill Linda Stamper

Keystrokes for TI-30X IIS 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: 2nd √ 4 = 2 4 √ = 2 Keystrokes for TI-30X IIS Keystrokes for TI-30X A

Evaluate the expression. Give the exact value, if possible 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 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 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 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 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 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 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.

There are two solutions (roots): 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):

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 Example 13 Example 16 Example 14 Example 15 Hint: Isolate the squared term on one side of the equal sign.

Solve the equations. Write the solutions as integers if possible 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 Solve the equations. Write the solutions as integers if possible. Otherwise, round to the nearest tenth. Example 13 Example 14

Solve the equations. Write the solutions as integers if possible Solve the equations. Write the solutions as integers if possible. Otherwise, round to the nearest tenth. Example 15 Example 16

Homework 9-A5 Handout A5.