How Do Changes in a, b, and c Values Affect the Graph of a Quadratic Equation?

[roger]

Dear members,

For the general equation ax^2 + BX + C = 0 ,

what does increasing/decreasing the a, b and c values do to the graph ?

Are they related to each other or not ?

If C was 0 will the graph always be symmetrical about the origin or is this my misunderstanding ?


Thankyou for any help.

From Roger

 

[Gokul43201]

Dear members,

For the general equation ax^2 + BX + C = 0 ,

what does increasing/decreasing the a, b and c values do to the graph ?

Increasing a or c will increase the value of the function, for all x. But increasing b will increase the value of the function for positive x, but decrease it for negative x. Figure out for yourself, why this is true.

If C was 0 will the graph always be symmetrical about the origin or is this my misunderstanding ?

It is a misunderstanding. But if b=0, the graph will be symmetrical. Here's you you figure it out : y(x) = ax^2 + bx + c. What is y(x) if b=0 ? Now what is y(-x), with b=0 ? Compare these.

 

[ambuj123]

Actually
if you take f(x)=ax^2 + bx + c as equation of parabola and then investigate it will be much eaqsier.
if a>0 the parabola open's upward and if a < 0 parabloa opens downward.
now if c=0 then above reduces to
y =ax(x+b)
which means vertex of parabola shifts to a position whose x coordinate -is -b (ii suppose not sure about this)
if d=0
the b^2=4ac the parabola touches x-axis and point where it touches x-axis is only solution of equation.
similarly you can find other cases

 

[Integral]

Do you have access to Excel or some other spread sheet? The best way to learn what those constants do is draw some pictures. You easily do this in excel, with little effort you could change a parameter and immediately see the graph change.

 

[ambuj123]

Can you help me draw graph of quadratic functions in excel ?

 

[robphy]

It may be good to consider a physical analogy... namely a particle undergoing constant acceleration: x=At²+Bt+C,
where A=a/2 "half of the acceleration",
B=v₀ "initial velocity",
and C=x₀ "initial position".

C is the intercept on the vertical axis.
Increasing C, translates the parabola upward.
B is the slope of the tangent at the intercept.
Varying B can be pictured this way: while maintaining the intercept, translate the parabola, which effectively varies the slope of the tangent at the intercept.
Varying A changes the "curvature" in some sense.

 

[HallsofIvy]

An EQUATION, such as ax²+ bx+ c= 0 does NOT have a "graph". If you meant the graph of the function y= ax²+ bx+ c, that'ws a whole different matter.