Q. 83 - Precalculus Enhanced with Graphing Utilities

Question

The equation $y={\left(x-c\right)}^2$ 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

$c=-2$.

Step-by-Step Solution

Answer

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

Step 1 Given values are, c = 0 , c = - 2 , c = 3 .

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

Substitute $c=0$ in the given equation.

$y=x^2$ which is the square function.

Substitute $c=-2$ in the equation.

$y={\left(x+2\right)}^2$, 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.

$y={\left(x-3\right)}^2$,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.