Assignment 2Examining the graphs of Different values of

a,b, andcaffect the graph of y in a different way. First of all,ahas to be different from 0. Otherwise, we get a linear function instead of quadratic.

1. Here is the graph of where

a= 1,b=0, andc= 0.This is the basic graph with

a=1,b=0 andc=0. We will talk about changes to this graph as we change the values ofa,b, andc.2. Keeping

b= 0, anda= 1, and varyingc, we can see the change in as follows.

Movement along the y-axis by one unit. When

c= 1, the graph moves up by one unit. And whenc= -1, the graph moves down by one unit.3. Keeping c = 0, and a = 1, and varying b, we can see the change in as follows.

One of the x-intercepts has moved to the right and the other one to the left by one unit. The vertex has also moved down by 1/4.

4. Keeping

b= 0 andc= 0 and varyinga, the change in as follows.When

a= 1/2, the graph is a lot wider than whena= 2. Also when a = -1, the graph is inverted upside down.5. Similarly we can also look at when

is aperfect square for different values ofh.Movement along the x-axis. When h = 1, the graph moves one unit to the left and when h = -1, the graph moves one unit to the right.

ConclusionThe graph of

is affected differently when we use different values ofa,b, andc. For y to be a quadratic function,ahas to be different from 0. Compared to the graph of , when a = -1, b = 0 and c 0, the whole graph is inverted upside down. In other words, the graph is just the mirror image of that of across the x-axis. Keeping a = 1 and b = 0, and varying c, we can see that the graph of moves up along the y-axis by c units or moves down by c units if c is negative. If we keep c = 0, a = 1 and vary b, we can see that the x-intercepts change. It adds one more x-intercept and also moves the vertex of the graph ofdown. Similarly, varying

aand keeping the other two constant will have an effect in the width of the graph. The graph is a lot wider when |a| < 1 than at any other time. We can also look at whenis aperfect square for different values ofh. It moves the graph of |h| units to the right or to the left on the x-axis. When h is positive, the graph moves to the left and when h is negative, the graph moves to the right on the x-axis.