Multiply out the vertex form (y= a(x-h)^2 + k). Compare the h and k to the a, b, and c in the standard form (y=ax^2 +bx+c). What information do the parameters or combinations of parameters provide about the graph of the quadratic function?

Question

anonymous · Answer

I am desperate and really need help! Would appreciate any help given.

joannablackwelder · Answer

Multiply everything out and try to make the equation look as much like ax^2 +bx + c as possible.

joannablackwelder · Answer

a(x-h)(x-h) +k

joannablackwelder · Answer

a(x^2 - 2xh + h^2) + k

joannablackwelder · Answer

Make sense so far?

anonymous · Answer

Yes. I got the same thing today. Now all I had to compare was standard form to what we got. So c=ah^2+k  ax^2=ax^2 h+k= a+b+c. The question says to compare h and k to the a,b and c in standard form. IT also says what information does the parameters give us about the quadratic function. Is there anything else that I can add into my answer?

joannablackwelder · Answer

I got that a=a, b=-2ah, and c=ah^2+k

joannablackwelder · Answer

So, since the width of the parabola is determined by the leading coefficient of standard form, the h and k do not affect that term and thus don't affect the width of the graph.

anonymous · Answer

Is that the final answer?

joannablackwelder · Answer

That is the only thing I can think of. Not sure if your teacher is looking for something else...

joannablackwelder · Answer

@abb0t  Any thoughts?

abb0t · Answer

Did you foil it out?

anonymous · Answer

That Answers my question thanks for the help!