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i have questions about parts of the parabola standard form. I know that it is ax^2+bx+c but what does b and c represent.

Guest Feb 17, 2018
 #1
avatar+91027 
+1

a  =   the width of the parabola

If  l a l < 1...the graph is wider than the graph y = x^2, if  l a l > 1....the graph is narrower than the graph y =  x^2  and if a < 0....we have an "upside" down parabola

 

c  =  the y intercept

 

b...when this isn't 0,  it shifts the vertex of the graph off of the y axis....either left or right

 

 

Look at these graphs to get a feel for this :

 

https://www.desmos.com/calculator/shyvwfty0k

 

 

cool cool cool

CPhill  Feb 17, 2018
 #2
avatar
0

Is b important then? My problem is with b.

Guest Feb 17, 2018
 #3
avatar+91027 
0

Yes...without  "b,"  all vertcal parabolas would have a vertex on the y axis....but, of course, the vertex can definitely be away from the y axis

 

 

cool cool cool

CPhill  Feb 17, 2018
 #4
avatar+20146 
0

what does b  represent?


\(\begin{array}{|lrcll|} \hline &y &=& ax^2+bx+c \\ &y' &=& 2ax+b \\ x=0: &y' &=& b \\ \hline \end{array} \)

 

so b is the slope at x = 0.

 

laugh

heureka  Feb 19, 2018

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