Problem 2
Graph
Fix two of the values for a, b, and c. Make at least 5 graphs on the same axes as you vary the third value.
First we will set a = 1 and b = 1 and set the value of c = -10, -5, 0, 5, and 10.
Looking at the graph we notice that as we change c the shape of the graph remains the same, what changes is the location of the graph. The vertex moves vertically when c is changed. When c is negative the vertex of the graph is below the x-axis.
Next, we will set a = 1 and c = 1 and set the value of b = -6, -3, 0, 3, and 6.
Looking at this graph we notice that as b changes the shape of the graph remains the same, but the graph moves horizontally and vertically. When b is negative the vertex of the graph is to the right of the y-axis and when b is positive the vertex of the graph to the left of the y-axis. When b=0 the vertex is on the y-axis.
Next, we will set b = 1 and c = 1 and set the value of a = -10, -5, 0, 5, and 10.
Looking at the graph we notice that as a changes, the shape of the graph changes. When a is positive the graph is a parabola that opens up and when a is negative the graph is a parabola that opens down. We also notice that if a equals zero the graph becomes a straight line. When a = 0 the equation becomes y = x +1 which is a linear equation. It is also noticed that all graphs pass through the point (0,1). Any equations in this form will pass through the point (0,c).