U4-S3-L3 Solve Quadratics by Square Roots

Essential Question: How do you solve a quadratic equation by graphing and square roots?

Solving

• To solve a quadratic function, look for the x-intercepts: where the parabola intersects the x-axis.

• Words for solutions to quadratics:Words for solutions to quadratics:1) zeros1) zeros

• 2) roots2) roots• 3) solutions3) solutions• 4) answers4) answers• 5) x-intercepts5) x-intercepts

Solutions

• A zero is just like looking for an x-intercept• A quadratic will only have 2, 1, or no zeros.

Solving by Graphing

Practice

1) x2 - 9 = 0 2) -½ x2 + 1 = 0

Main Idea

• Some quadratic equations are missing an a, b, or c value, and graphing can be difficult.

• You can solve by square roots.• Remember, you cannot take the square root

of a negative number.• However, there are 2 answers to a square

root: the positive and negative root.

VocabularyVocabulary

• Perfect SquarePerfect Square: A number whose square roots are integers.

• Square RootSquare Root: one of the equal factors that makes up the square.– Uses the “√ ” symbol– Has a positive and negative solution

• Principle Square RootPrinciple Square Root: the positive square root

Squares & Square Roots

• Squares and square roots are inverse operations because they are opposites.

Finding Squares

• List the squares up to 30.12 = 112 = 212 =

22 = 122 = 222 =

32 = 132 = 232 =

42 = 142 = 242 =

52 = 152 = 252 =

62 = 162 = 262 =

72 = 172 = 272 =

82 = 182 = 282 =

92 = 192 = 292 =

102 = 202 = 302 =

Finding Squares

• List the squares up to 30.12 = 1 112 = 121 212 = 441

22 = 4 122 = 144 222 = 484

32 = 9 132 = 169 232 = 529

42 = 16 142 = 196 242 = 576

52 = 25 152 = 225 252 = 625

62 = 36 162 = 256 262 = 676

72 = 49 172 = 289 272 = 729

82 = 64 182 = 324 282 = 784

92 = 81 192 = 361 292 = 841

102 = 100 202 = 400 302 = 900

Solving by Square Roots

• To solve by square root:1)Quadratic does NOT have a b. Only ax2 + c = 02)Isolate the variable by inverse operations.3)Square root both sides, if possible.4)Write solution as + and – answer.

Practice

Simplify, then Root

1)1) Isolate xIsolate x22

2)2) Take the square root of both sidesTake the square root of both sides

Practice

Approximating Solutions

• When factoring doesn’t work, and it isn’t a perfect square, then you must round your answer.

Summary

• Answer the essential question in detailed, complete sentences.

• How do you solve a quadratic equation by graphing and square roots?

• Write 3-5 study questions in the left column to correspond with the notes.