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# Module16!

### Solving Quadratic Equations by Completing the Square

Question | Answer |
---|---|

What is the Square Root Property? | If <i>b</i> is a real number and a^2=b, then a=-√b and a=+√b |

What does +/-4 mean? | "Plus or minus four" |

Use the Square Root Property to solve and check x^2=36 | x^2=36 = √x^2=√36 = x=+/-6 -ALWAYS CHECK YOUR ANSWERS! |

Use the Square Root Property to solve and check x^2-16=0 | x^2-16=0 = x^2=16 = √x^2=√16 = x=+/-4 -ALWAYS CHECK YOUR ANSWERS! |

Use the Square Root Property to solve and check (2x-5)^2=-16 | √(2x-5)^2=√-16 = 2x-5=+/-4i = x=5+/-4i/2 FINAL ANSWER: 5+4i/2 and 5-4i/2 |

To Complete the Square, you must first: | Add the square of half the coefficient of <i>p</i> to both sides to make a perfect square trinomial. |

Complete the Square: b^2+4b | b^2+4b= (4*.5)^2 =2^2=4, SO: b^2+4b+4 is the perfect square trinomial, now FACTOR: (b+2)^2=0, THEN: √(b+2)^2=√0, b=-2 |

Solve by Completing the Square: 2x^2-8x+3=0 | Divide by 2: 2x^2/2-8x/2=-3/2, x^2-4x=-3/2, THEN: (4*.5)^2=4, SO: x^2-4x+4=11/2 AND: (x-2)^2=11/2 NEXT: √(x-2)^2=√11/2, FINALLY: x=2+/-√11/2 |

What types of problems does the text list that can be modeled after Quadratic Equations and solved? | Interest Problems, including compound interest, simple interest, and interest rate calculations |

What do the formulas I=Prt AND A=P(1+r)^t help to solve? | Simple and Compound Interest problems |

Using A=P(1+r)^t, Solve: Find the interest rate r, if $4000 compounded annually grows to $4540 in 2 years. | 4540=4000(1+r)^2 DIVIDE: 4540/4000=4000(1+r)^2/4000 SO, 1.135=(1+r)^2 SQUARE ROOT PROPERTY: √1.135=√(1+r)^2 EQUALS: +/-1.06=1+r, -1+/-1.06=r, SO NOW: KEEP -1+1.06=0.06 to find: r=6% |

Calculate the Simple Interest Problem using I=Prt: $2,000 is invested at the simple interest rate 5% annually for 1 year. | I=2000*.05*1 SO: I=100 The simple interest earned in 1 year is $100, bringing the annual total to $2,100 |

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