Use complete sentences to describe the transformations that were done to the parent function F(x)=X^2 to create g(x)=-2(x-6)^2 +5.
see "klara" post at 4:06 pm
F(x) = x^2
---> -x^2 , it was reflected in the x-axis
---> -2x^2 , it was stretched vertically by a factor of 2
---> -2(x-6)^2 , now we made a horizontal shift of 6 units to the right
---> -2(x-6)^2 + 5 , finally, we made a vertical shift of 5 units upwards
To describe the transformations done to the parent function F(x) = x^2 to create g(x) = -2(x - 6)^2 + 5, we can break it down into three main transformations:
1. Vertical Reflection: The negative sign in front of the original function (-2) reflects the graph of F(x) = x^2 vertically over the x-axis. This means that any point on the graph that was originally above the x-axis will now be below the x-axis, and vice versa.
2. Horizontal Translation: The function is shifted horizontally 6 units to the right. This is indicated by the (x - 6) term inside the parentheses. So, instead of the vertex being at the origin (0,0), it is now located at (6,0).
3. Vertical Translation: The function is shifted vertically 5 units up. This is indicated by the +5 at the end of the function. So, the entire graph of g(x) is shifted 5 units higher compared to F(x).
Putting it all together, the function g(x) = -2(x - 6)^2 + 5 represents a vertical reflection, horizontal translation of 6 units to the right, and a vertical translation of 5 units up when compared to the parent function F(x) = x^2.