Describe how the graph of a quadratic equation changes as the values of a,b, and c change in the equation..?

Question

ax^2 + bx + c = 0.?

Answer 1

ax^x +bx + c (where a, b and c are coefficients)
a = is to decide either how the parabola will look like, either u-shape or n-shape (the shape will turn to u-shape if the value for "a" is positive, and the parabola will turn into n-shape if the value of "a" is negative)
b = is the intersection at x-axis, usually have two values of x or sometimes none
c = is the y-axis intercept (if there are no "c", then the other side of the parabola will cross at the origin point, 0)

Answer 2

I assume that you mean how the values of a, b, c affect the graph of y = ax^2 + bx + c because as written you just have a quadratic equation.
The 'a' not only determines whether the curve will appear as a U or upside down U but also how steep it will be. High values of 'a' make the curve a very narrow U and low values make it very wide.
The 'c' is the y intercept and so increasing 'c' moves the curve upwards and decreasing it moves the curve downwards. However the 'b' is not the x intercept. It is involved in the position of the vertex of the curve which is -b/2a. Thus increasing b will move the curve to the left and decreasing it will move the curve to the right. However changes to 'a' will also have this effect.
The x intercepts are found by the quadratic formula which of course involves all three coefficients.