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.
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.
Simplify, then Root
1)1) Isolate xIsolate x22
2)2) Take the square root of both sidesTake the square root of both sides
Approximating Solutions
• When factoring doesn’t work, and it isn’t a perfect square, then you must round your answer.