To determine the quadratic function that is obtained from the parent function, consider the transformations one at a time.
Rule: g(x)=-4x^2+2 Vertex: (0,2)
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 Stretch by a Factor of 4
We will start by performing a vertical stretch on the parent function by a factor of 4. This is done by multiplying the parent function by 4. The resulting function is y=4x^2.
Reflection in the x-axis
Next, let's reflect the function across the x-axis by multiplying the whole function by - 1.
y=4x^2 ⇔ y=-4x^2
Let's draw the graph of this function.
Vertical Translation 2 Units Up
Finally to perform a vertical translation 2 units up, we need to add 2 to the whole function. The result is g(x)=-4x^2+2.
The quadratic function that is obtained after the sequence of transformations is g(x)=-4x^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 stretch
(x, 4y)
Reflection in the x-axis
(x, -4y)
Vertical translation up
(x,-4y+ 2)
Let's substitute the coordinates of a parent function to find the new vertex.
