My teacher wants me to make 5 hard complete the square questions and solve them in front of her to get a %5 bonus mark. Can anyone give me 5 really hard complete the square questions?
See what you can find here:
http://www.google.com/search?sourceid=navclient&ie=UTF-8&rlz=1T4VRHB_enUS648US649&q=complete+the+square+questions
The hardest type have fractional coefficients that are relatively prime.
I will give you one, and solve it, you pick 4 more like it
y = (2/3)x^2 + (5/7)x - 11/13
factor the coefficient (divide it out) of the x^2 terms from the first two terms, leave the constant term trailing along at the end
= (2/3)(x^2 + (15/14)x ...... ) - 11/13
take 1/2 of the x term coefficient, square it, then add and subtract in side the bracket
= (2/3)(x^2 + (15/14)x + 225/784 - 225/784) - 11/13
the first 3 terms inside the bracket are now a perfect square, write it that way, but don't forget the -225/784 inside the bracket and the -11/13 just hanging on at the end
= (2/3)( (x + 15/28)^2 - 225/784) - 11/13
you now have two terms inside the main bracket, multiply 2/3 by both of them
= (2/3)(x+15/28)^2 - 75/392 - 11/13
all we have to do in combine the two constants at the end, the common denominator is 5096
= (2/3)(x + 15/28)^2 - 975/5096 - 4312/5096
= (2/3)(x + 15/28)^2 - 5287/5087
check my arithmetic
Of course! Here are five challenging complete the square questions for you:
1. Solve: x^2 + 8x + 15 = 0
To complete the square, take half of the coefficient of the x term, square it, and add it to both sides of the equation.
2. Solve: 2x^2 + 4x - 3 = 0
Again, apply the complete the square method by adding the square of half the coefficient of the x term to both sides.
3. Solve: 3x^2 - 10x + 4 = 0
Follow the complete the square method by adding the square of half the coefficient of the x term to both sides.
4. Solve: 4x^2 - 12x + 9 = 0
You can complete the square on this equation by adding the square of half the coefficient of the x term to both sides.
5. Solve: 5x^2 + 2x - 1 = 0
Once again, apply the complete the square method by adding the square of half the coefficient of the x term to both sides.
Remember to show your work when solving these equations in front of your teacher to earn your bonus mark!