Hi. I need help for an upcoming test tomorrow. I did some practice problems, can you guys please check if they're right? And if not, can you please do it and show me your work? I feel like I get the basic concept but I'm missing a few steps.
Complete the square for each expression. Write the resulting expression as a binomial squared.
23.
My answer
24. x^2 + 10x + _
My answer
25.
My answer
Solve each equation by completing the square (I feel I got these questions wrong)
26.
My answer
27.
My answer
I will also post questions about writing each function in vertex form, but right now I'm focused on this. Can you guys please see if I got anything wrong and if I did, can you please show me how you got the right answer? Also, it would be nice if you guys could explain it or even show a video. This is a great community and I would like to thank everybody who contributes on this website!
Thank you "Prove It." I will rework the problems and try them again. If I'm getting this right, the only thing I'm doing wrong is not adding the constant at the end? So the answers would be:
23. (x-9)^2 -81
24. (x+5)^2 +25
25. (x+1/4)^2 + 1/6
You're supposed to subtract the constant, not add it. Try expanding your results and collecting like terms to check your answer.
I don't think you understand what is happening when you complete the square. You are adding a CLEVERLY DISGUISED ZERO, since adding zero does not change its value.
Anyway, looking at the general case for a monic quadratic
Notice that the coefficient of and the constant have something in common, .
So that means if you only had the first two terms of the quadratic, you could use the second term to find the constant.
Notice that to turn into , you need to HALVE it, then SQUARE it.
But remember that you are planning to add ZERO, so whatever you do add, you need to then subtract.
So let's look at an example.
We need to halve and then square the coefficient of . This will be what we add and subtract.
Another example:
We need to halve and square the coefficient of . This will be what we add and subtract.
Another example: . Notice that the coefficient of is negative. This doesn't change the process, but we do need to remember that the negative is there. Anyway, adding and subtracting half of the coefficient of gives
And a final example, I hope you've noticed that completing the square only works for monic quadratics (i.e. where the coefficient of is 1). What happens if it's something else? You need to take it out as a common factor first. So using as an example...
So now you need to fix your answers.