Answer:
The quadratic function family; the parent function has a vertex at (0,0) while the new function is shifted up 3 and is skinnier than the parent function, it's parabola concaves down.
Step-by-step explanation:
Because it has x^2 in it which means it is a quadratic; a parent function is the original graph so the new function of f(x)= -2x^2+3 is negative, skinnier, and the vertex is shifted up 3 spaces.
A function can be transformed to another through dilation, reflection, translation and rotation. [tex]f(x) = -2x^2 + 3[/tex] belongs to the quadratic family. The following is the comparison of [tex]f(x) = -2x^2 + 3[/tex] and its parent function [tex]f(x) = x^2[/tex]
Given that:
[tex]f(x) = -2x^2 + 3[/tex]
To identify the function family, we do the following
When there is no negative exponent and the highest power of the variable is 2, then the function belongs to the quadratic family.
Next, we compare the function to its parent function.
The parent function of a quadratic function is:
[tex]y = x^2[/tex]
First, the parent function is vertically stretched by 2. The rule of this transformation is:
[tex](x,y) \to (x,2y)[/tex]
So, we have:
[tex]y' = 2x^2[/tex]
The function is then rotated along the x-axis. The rule of this is:
[tex](x,y) \to (x,-y)[/tex]
So, we have:
[tex]y" = -2x^2[/tex]
Lastly, the function is translated up by 3 units. The rule of this is:
[tex](x,y) \to (x,y+3)[/tex]
So, we have:
[tex]f(x) = -2x^2 + 3[/tex]
In conclusion:
See attachment for both functions
Read more about function transformations at:
https://brainly.com/question/3333365
