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Module16!

Solving Quadratic Equations by Completing the Square

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
Created by: 1116100094