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Mathematics 51 Online
OpenStudy (anonymous):

Write the given quadratic function y=ax²+bx+c to its equivalent standard form y=a(x-h)²+k. 1.) y=x²-x+13/4 2.) y=1/2x²-3x+3 3.) y=-2x²+12x-17 4.) y=x²-4x+1 5.) y=2x²-4x+4 what mathematics concept did you use in doing the transformation ? explain how quadratic function in the form y=ax²+bx+c can transformed into the form y=a(x-h)²+k. PLEASE I NEED HELP !

OpenStudy (ahsome):

You would need to use Completing the Square Do you want an example?

OpenStudy (anonymous):

yes..

OpenStudy (anonymous):

please .. help me ... @ganeshie8 @Ahsome

OpenStudy (ahsome):

Ok

OpenStudy (ahsome):

Let's do this equation: \[ y=x^2-x+\frac{13}{4}\]

OpenStudy (ahsome):

Have you heard of completing the square before?

OpenStudy (anonymous):

sorry i haven't ..

OpenStudy (ahsome):

Thats gonna be hard

OpenStudy (ahsome):

Have you done this before: \[(a+b)^2=a^2+2ab+b^2\]\[(a-b)^2=a^2-2ab+b^2\]

OpenStudy (anonymous):

yeah ..

OpenStudy (ahsome):

Ok. Completing the square is used to make any equation into that form, so it is easier to simplify.

OpenStudy (ahsome):

Equation: \[y=x^2-x+\frac{13}{4}\] Now, to complete the square, we need to make a number. We get this number by doing: \[(\frac{b}{2})^2\]

OpenStudy (ahsome):

What is the \(b\) value in this equation?

OpenStudy (anonymous):

it's 1.

OpenStudy (ahsome):

no, its -1. Can you see that?

OpenStudy (anonymous):

oh sorry .. then ?

OpenStudy (ahsome):

Ok. Sub that value to the equation: \[(\frac{b}{2})^2\] \[(\frac{-1}{2})^2\] \[0.25\]

OpenStudy (ahsome):

Add that number to the equation after the \(x\) \[y=x^2−x+0.25+\frac{13}{4}\] The issue here is that we can't simply just add a number and not change the value. So we need to subtract the same vaule to even it out. I will do that into the end of the equation: \[y=x^2−x+0.25+\frac{13}{4}-0.25\]

OpenStudy (ahsome):

Does that make sense?

OpenStudy (anonymous):

after that ?

OpenStudy (ahsome):

Now. can you see this section: \[x^2-x+0.25\] That part resembles this section: \[a^2-2ab+b^2\] Which we know can simplify to: \[(a-b)^2\] Therefore, we can simplify the equation: \[y=x^2-x+0.25+\frac{13}{4}−0.25\] To: \[y=(x-0.5)^2+\frac{13}{4}−0.25\] Simplify the rest \[y=(x-0.5)^2+3\] Tada. we have now transformed it into standard form :D

OpenStudy (anonymous):

thanks @Ahsome . i'll just solve the remaining .. :D thanks for the help ..

OpenStudy (ahsome):

No problem @heizl46. If you didn't understand anything, just say so!

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