CCA Averages Second Period Fourth Period Sixth Period Seventh Period Eighth Period

CCA Answers 1.D 2.G 3.A 4.H 5.C 6.F 7.D 8.H 9.B 10.H 11.C 12.J 13.B 14.H 15.B 16.J 17.D 18.G 19.D 20.H

Solving Quadratic Equations

Quadratic Equations A quadratic equation is an equation that can be written in the standard form: ax² + bx + c = 0 Quadratic equations will have zero, one, or two solutions.

To Solve A Quadratic Equation When b = 0… Use the same procedures you used to solve an equation to get the “x” isolated (by itself). Instead of having an “x” left, you have an “x²”. When the “x²” is isolated, find the square root of both sides (be sure to give both the principal and the negative roots!).

Example 1 Solve:2x² - 18 = 0 Add 18 to both sides2x² = 18 Divide both sides by 2x² = 9 Find the square root of both sides x = ± 3

Example 2 Solve:2x² + 72 = 0 Subtract 72 from both sides 2x² = -72 Divide both sides by 2x² = -36 Find the square root of both sides— oops!! You can’t find the square root of a negative number (-36) so there is NO SOLUTION!

Example 3 Solve:2x² + 8x² + 16 = 32 Simplify:10x² + 16 = 32 Subtract 16 from both sides10x² = 16 Divide both sides by 10x² = 1.6 Find the square root of both sides X = ± … round to the hundredth’s place X = ±1.26

Find the quadratic function whose solutions are 4 and -3. x = 4 and x = -3 x – 4 = 0 and x + 3 = 0 (x – 4)(x + 3) = 0 FOIL x 2 –x – 12 = 0

Find the quadratic function whose solutions are -1 and ½. x = -1 x + 1 = 0 (x + 1)(2x – 1) = 0 FOIL 2x 2 + x - 1 x = ½ Multiply by 2 to get rid of the fraction. 2x = 1 2x – 1 = 0

Things to think about…. When will there be two solutions? When will there be one solution? When will there be no solutions? Look at the graphs of each type of equation listed above. Can you tell by looking a the graph?

Try these… 4x = 17 Find the radius of a circle whose area is 125 in 2. 81x = 0 3x 2 – 85 = 2x 2 – 36 4x = 2x x = ± 2 r = 6.31 in x = ± 7/9 x = ± 7 No real solution