Assignment #2
Nicole Mosteller
EMAT 6680
Question #6 of Investigation #2 begins with an ordinary quadratic equation

that produces the parabola in Figure 1.

From previous investigations, we know how each of the coefficients (2, 3, -4) effect the shape of the basic parabola (changes the width of the sides, makes concave up or down, changes the location of the vertex, shifts up or down). This assignment requires an additional investigation on the parabola which allows us to see what makes a parabola shift left and right.

6i. Overlay a new graph replacing each x by (x - 4). See Figure 2 for the results.

Figure 2:

By changing the value of x to (x - 4), we see that the first parabola has shifted to the right four spaces. Why does this happen? Let's investigate the basic equation for a parabola

.

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6ii. Change the equation to move the graph into the second quadrant.

To make this move, we will change both the value of k so that the graph shifts left and the value of c so that the graph shifts up. See Figure 2 for the results.

Figure 3: Let k = -4 and c = +4.

6ii. Change the equation to produce a graph concave down that shares the same vertex.

Figure 4: The new graph  is the graph of the equation
,
but flipped at the vertex. For explanation, see attached page.