Thread: Quadratic Equations and Forms

If I have a relation in Vertex form, how do I make it into standard form?

y = a(x-h)^2 + k into y = ax^2 + bx +c

Example questions:
a) y = 5(x+3)^2 -2
b) y = 2x(5-2x)+7


I'm not exactly looking for the answers, I just want to understand HOW to solve these.

Please help!


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heres my solution to question a, if you could advise me that would be much appreciated!

y = 5(x+3)^2 -2
= 5(x^2+9x-9)-2
= 5(x^2+9x)-2+9
= 5x^2 + 9x + 7

Originally Posted by Namis9

If I have a relation in Vertex form, how do I make it into standard form?

y = a(x-h)^2 + k into y = ax^2 + bx +c

Example questions:
a) y = 5(x+3)^2 -2
b) y = 2x(5-2x)+7


I'm not exactly looking for the answers, I just want to understand HOW to solve these.

Please help!


----------------------

heres my solution to question a, if you could advise me that would be much appreciated!

y = 5(x+3)^2 -2
= 5(x^2+9x-9)-2
= 5(x^2+9x)-2+9
= 5x^2 + 9x + 7

You have the method, but some mistakes in your work:
y = 5(x+3)^2 -2

y = 5(x^2 + 6x + 9) - 2

y = 5x^2 + 30x + 45 - 2

y = 5x^2 + 30x + 43

-Dan

Originally Posted by topsquark

You have the method, but some mistakes in your work:
y = 5(x+3)^2 -2

y = 5(x^2 + 6x + 9) - 2

y = 5x^2 + 30x + 45 - 2

y = 5x^2 + 30x + 43

-Dan

Thanks, I now understand what I did wrong. Much Appreciated!

For the second question, where you are not squaring the brackets I am a little confused. Perhaps you can help me as well? I'm not even exactly sure where to start on this.

y = 2x(5-2x)+7 into y=ax^2 + bx + c

Originally Posted by Namis9

Thanks, I now understand what I did wrong. Much Appreciated!

For the second question, where you are not squaring the brackets I am a little confused. Perhaps you can help me as well? I'm not even exactly sure where to start on this.

y = 2x(5-2x)+7 into y=ax^2 + bx + c

Sorry, I didn't realize you hadn't spotted what you are trying to do.

All you are up do in this sort of thing is expanding the quadratic into its separate terms.

In this case just multiply it out:
y = 2x(5-2x)+7

y = 10x - 4x^2 + 7

y = -4x^2 + 10x + 7

This is far easier than taking y = ax^2 + bx + c and going to y = a(x - h)^2 + k. All you need to do is expand out all the terms and simplify.

-Dan

Thank you very much

You've helped me a lot.