Respuesta :
Transformation of a function is shifting the function from its original place in the graph.
The functions have a maximum and are transformed to the left and down of the parent function are,
[tex]q(x) = -5(x +10)^2 -1[/tex]
[tex]t(x) = -2x^2 - 4x - 3[/tex]
Thus the option B and E is correct.
What is transformation of a function?
Transformation of a function is shifting the function from its original place in the graph.
Types of transformation-
- Horizontal shift- Let the parent function is [tex]f(x)[/tex]. Thus by replacing parent function with [tex]f(x-b)[/tex] shifts the graph b units right and by replacing parent function with [tex]f(x+b)[/tex] shifts the graph b units left.
- Vertical shift- Let the parent function is [tex]f(x)[/tex]. Thus by replacing parent function with [tex]f(x)-c[/tex] shifts the graph b units down and by replacing parent function with [tex]f(x)+c[/tex] shifts the graph b units up.
Given information-
The given function in the problem is,
[tex]f(x)=x^2[/tex]
The functions have a maximum and are transformed to the left and down of the parent function.
In the option B the function is shifted 10 units left and 1 units down as,
[tex]q(x) = -5(x +10)^2 -1[/tex]
Thus the option B is the correct option.
In the option E the function is shifted 1 units left and 2 units down as,
[tex]t(x) = -2x^2 - 4x - 3\\t(x)=-2x^2 - 4x - 1-2\\t(x)=-2(x+1)^2-2[/tex]
Thus the option E is the correct option.
Hence, the functions have a maximum and are transformed to the left and down of the parent function are,
[tex]q(x) = -5(x +10)^2 -1[/tex]
[tex]t(x) = -2x^2 - 4x - 3[/tex]
Thus the option B and E is correct.
Learn more about the transformation of a function here;
https://brainly.com/question/10904859
