Chapter 2: Q. 83 (page 114)

The equation $y = {(x - c)}^{2}$ defines a family of parabolas, one parabola for each value of $c$ . On one set of coordinate axes, graph the members of the family for $c = 0, c = 3$ and
$c = - 2$ .

Short Answer

Expert verified

The graph for the parabolas when $c = 0, c = - 2, c = 3$ is,

Step by step solution

Step1 Given values are, c=0,c=-2,c=3.

Given equation is, $y = {(x - c)}^{2}$

Substitute $c = 0$ in the given equation.

$y = x^{2}$ which is the square function.

Substitute $c = - 2$ in the equation.

$y = {(x + 2)}^{2}$ , the graph of which is obtained by shifting the graph of $y = x^{2}$ to the left by $2$ units.

Substitute $c = 3$ in the equation.

$y = {(x - 3)}^{2}$ ,the graph of which is obtained by shifting the graph of $y = x^{2}$ to the right by $3$ units.

Step 2 Now graph the obtained equations.

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The equation $y = {(x - c)}^{2}$ defines a family of parabolas, one parabola for each value of $c$ . On one set of coordinate axes, graph the members of the family for $c = 0, c = 3$ and
$c = - 2$ .

Short Answer

Step by step solution

Step1 Given values are, c=0,c=-2,c=3.

Step 2 Now graph the obtained equations.

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The equation y=x-c2defines a family of parabolas, one parabola for each value of c. On one set of coordinate axes, graph the members of the family for c=0,c=3andc=-2.

Short Answer

Step by step solution

Step1 Given values are, c=0,c=-2,c=3.

Step 2 Now graph the obtained equations.

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

The equation $y = {(x - c)}^{2}$ defines a family of parabolas, one parabola for each value of $c$ . On one set of coordinate axes, graph the members of the family for $c = 0, c = 3$ and
$c = - 2$ .