Assignment #2Nicole MostellerEMAT 6680

Question #6 of Investigation #2 begins with an ordinary quadratic equation that produces the parabola inFigure 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

**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.

LetFigure 3:k = -4andc = +4.

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

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