To determine the quadratic function that is obtained from the parent function, consider the transformations one at a time.
Rule: g(x)=1/3(x-3)^2 Vertex: (3,0)
Practice makes perfect
To determine the quadratic function that is obtained from the parent function f(x)=x^2 after the given sequence of transformations, let's consider the transformations one at a time.
Vertical Shrink by a Factor of 13
We will start by performing a vertical shrink on the parent function by a factor of 13. This is done by multiplying the parent function by 13. The resulting function is y= 13x^2.
Reflection in the y-axis
Next, let's reflect the function across the y-axis by multiplying the variable by -1.
y=1/3(- x)^2 ⇔ y=1/3x^2
Notice, in this case the function does not change because (- x)^2=x^2.
Horizontal Translation 3 Units Right
Finally, to perform a horizontal translation 4 units right we need to subtract 3 from the x-variable. The result is g(x)= 13(x-3)^2.
The quadratic function that is obtained after the sequence of transformations is g(x)= 13(x-2)^2.
Vertex
The vertex of the quadratic parent function is (0,0). We can find the vertex of g using the transformations found above.
Transformations
Change in coordinates
Vertical shrink
(x, 1/3y)
Reflection in the y-axis
( -x,1/3y)
Horizontal translation right
(- x+ 3,1/3y)
Let's substitute the coordinates of a parent function to find the new vertex.
