Chapter Closure
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What might the parent function be when there is binomial with a cubed x?
In what types of equations are both x and y squared?
There's an absolute value sign in the equation.
Parent Graph: y=x^3
Transformations: Shifted 8 units right, 2 units up, and compressed by 0.25.
Parent Graph: x^2+y^2=r^2
Transformation: Translation 3 units to the right and a dilation of the radius by a factor of 5.
Parent Graph: y=|x|
Transformation: Shifted 5 units to the right and 3 units up.
This equation is a cubic function which means we can write it in the following general format.
y= a(x-h)^3+k
Horizontal Translation:& h
Vertical Translation:& k
Vertical Stretch:& a
As we can see, the constants and the coefficient control different transformations of the parent function.
Next we will compress the graph by a factor of 0.25. The compression is done with respect to the horizontal line through the new locator point at (8,2). In other words, all points move closer to this horizontal line.
Examining the equation, we notice that it contains both a squared x and a squared y. This means it takes the shape of a circle, which has the following parent function.
x^2+y^2=1
The general equation for a circle can be written in the following format.
Next, we have to change the radius. The right-hand side of the equation is 25. By setting this equal to r^2, we can solve for the radius.
The radius is 5 units. With this information, we can carry out the final transformation.
This function contains an absolute value which means that y=|x| is its parent graph. We can write an absolute value function in the following general format.
y= a|x-h|+k
Horizontal Translation:& h
Vertical Translation:& k
Vertical Stretch:& a
