Question

Given a quadratic equation y = ax^2 + bx + c,

(i) What is the effect of changing the value of the number c on the parabola? In other word, if two parabolas have the same coefficients a, and b, but different values for c, how will their graphs differ?

My answer: If you have different values for c the y interecept would be different and depending on what number you would use for c depends on which way the y intercept would fall.

If you have a = 1, b = 2, x = 3, c = 4, then you would have y = 1(3)^2 + 2(3) + 4 = 9 + 6 + 4 = 19 (3, 19)
If you have a = 1, b = 2, x = 3, c= 0, then you would have y = 1(3)^2 + 2(3) + 0 = 9 + 6 = 15 (3, 15)

(ii) What is the effect of decreasing the value a toward 0 on the graph of the parabola?

My answer: The parabla sides would stretch out to one side,