Answer
A) If a > 0, parabola is facing up
If a = 0, parabola is becoming a straight line
If a < 0, parabola is facing down
B) if b = 0 the vertex lies on y-axis
When a > 0, if b → ∞ the graph shift left and down. And if b → -∞ the graph shift right and down.
When a < 0, if b → ∞ the graph shift toward right and up. And if b → -∞ the graph shift left and up.
C) If c → ∞, then y move vertical up, and if c → -∞, then y move vertical down.
Work Step by Step
A) Here, y= ax^{2}+ bx + c is an equation of parabola. So, if a > 0, then equation represents a parabola which is facing up. As the value of (a) increases, the parabola shrinks towards positive y-axis. If a = 0, then y = bx + c which is the equation represents a straight line. If a < 0, then the equation represents a parabola which is facing down and as the value of (a) decreases, it shrinks towards negative y-axis.
B) Here b changes and the value of a and c are fixed and moreover a≠0. Now, if b = 0, then the equation represents a parabola whose vertex lies on y-axis.
When a > 0, if b approaches to infinity, the graph of the equation will shift towards left and down simultaneously and as b approaches to minus infinity, the graph of the equation will shift towards right and down simultaneously.
When a < 0, if b approaches to infinity the graph of the equation will shift towards right and up simultaneously and as b approaches minus infinity the graph of the equation will shift towards left and up simultaneously.
C) Here, c changes and the value of a and b are fixed.
So, if c → ∞ (increasing) then y will move vertically up.
if c → −∞ (decreasing) then y will move vertically down.
