Answer
Equation (a) - Position 4
Equation (b) - Position 1
Equation (c) - Position 2
Equation (d) - Position 3
Work Step by Step
Here we would use the principles of graph shifting and examine each given equation to know how the graph has shifted from its original position.
We would take the original equation to be $y = x^2$.
You can take a look back at the blue graph at exercise 22 to know which position the graph of $y=x^2$ possesses. It collides the x-axis at $x=0$ and y-axis at $y=0$.
The equation after shifiting would have the form $$y=(x+a)^2+b$$ where $a$ and $b$ would give us clues as to how the original graph has shifted.
First, equation (a) $$y=(x-1)^2-4$$
$b=-4$ means the original graph of $y=x^2$ has shifted down 4 units.
$a=-1$ means the original graph also shifts to the right 1 unit.
That corresponds to Position 4, or the green graph.
Second, equation (b) $$y=(x-2)^2+2$$
$b=2$ means the original graph of $y=x^2$ has shifted up 2 units.
$a=-2$ means the original graph also shifts to the right 2 units.
That corresponds to Position 1, or the blue graph.
Third, equation (c) $$y=(x+2)^2+2$$
$b=2$ means the original graph of $y=x^2$ has shifted up 2 units.
$a=2$ means the original graph also shifts to the left 2 units.
That corresponds to Position 2, or the red graph.
Finally, equation (d) $$y=(x+3)^2-2$$
$b=-2$ means the original graph of $y=x^2$ has shifted down 2 units.
$a=3$ means the original graph also shifts to the left 3 units.
That corresponds to Position 3, or the yellow graph.
