Completing the Square Practice Questions

[valentines]

http://img114.exs.cx/img114/3245/untitled10ff.jpg

see if any of you guys can solve a few of these.. if you guys can show me the steps so that i can study them for any of my future tests that would be great.

 

[The Bob]

see if any of you guys can solve a few of these.. if you guys can show me the steps so that i can study them for any of my future tests that would be great.

16. Do you know what a parabola is?? Do you know what a vertex is?

17. Can you complete the square?

18. This is more of trial and error than a formula.

19. Pretend the 'more than or equal to' sign is an equal sign and then solve.

20. Can you use the quadratic equation or factorise?

If you know any of this I can start to help, if not I need to explain it.

The Bob (2004 ©)

 

[valentines]

16. Do you know what a parabola is?? Do you know what a vertex is?

17. Can you complete the square?

18. This is more of trial and error than a formula.

19. Pretend the 'more than or equal to' sign is an equal sign and then solve.

20. Can you use the quadratic equation or factorise?

If you know any of this I can start to help, if not I need to explain it.

The Bob (2004 ©)

nope. i have no idea what I am doing.


edit: actually, i know what a vertex is.

i don't know what a parabola is though

 

[The Bob]

A parabola is what you get when you draw the function y = x². Do you know what that looks like?

Lets say you have x² - 6x + 10. Completing the square would make the equation like this: (x - 3)² + 10 - 9 = (x - 3)² + 1. All that has happened is the -6x has been halved and put in brackets and then the new number (-3) has been squared and taken away from the 10.

Try completing the sqaure of x² - 10x + 30. Completing the sqaure is also needed for 19.

18. I would use the quadratic forumla : $$\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ but I think it will want you to complete the square.

Question 20 can be factorise from 2x² - 7x - 15 = 0 to (2x + 3)(x - 5) = 0 and then you have some values to use.

The Bob (2004 ©)

 

[The Bob]

I need to go sleep now but here are some completing the square question, for you, for practise and I am sure someone else will say if they are right or wrong for you:

y = x² - 8x + 20
y = x² - 4x + 7
y = x² + 2x + 2
y = x² + 4x + 2
y = x² - 10x + 25

Good Luck and I will read what you have done tomorrow.

The Bob (2004 ©)