Start out with the parent function y=|x| and translate/reflect it until it looks like the plot in the graphing calculator.
Equation: y=- |x+1|+1 Graphing calculator:
Practice makes perfect
Let's start out with the parent function y=|x| which has its vertex at (0,0).
Examining the calculator window, we see that its plot is upside down compared to the parent function. To turn the parent function upside down, we have to reflect it in the x-axis. This can be done by multiplying the absolute value by -1:
y=- 1* |x| ⇔ y=- |x|.Let's show the reflection of the parent function.
The plot from the calculator reaches its vertex at (- 1,1). To move the vertex from (0,0) to this location, we have to translate the graph vertically one step up by adding 1 to the function:
y=- |x| +1.
Finally, we have to translate the function horizontally one step to the left. To do that we add 1 to x:
y=- |x +1|+1.
Let's show these two translations.
This does resemble the plot in our graphing calculator. Let's plot it for ourselves to make sure. To enter the equation, we press Y= on our calculator and then write the equation on one of the rows.
Next, press GRAPH to plot the equation.
The calculator displays the standard viewing window. Let's change it to - 6≤ x ≤ 6 and - 4≤ y ≤ 4 and press GRAPH again to plot the equation.
