Answer:
The reflected across x-axis, stretched vertically by factor 3 and shifted 5 units right and 4 units up.
Step-by-step explanation:
The parent function is
[tex]f(x)=x^2[/tex]
The given function is
[tex]f(x)=-3(x-5)^2+4[/tex] ... (1)
The transformations of a quadratic function is defined as
[tex]f(x)=k(x+a)^2+b[/tex] .... (2)
Where, k is vertical stretch or compression factor, a is horizontal shift and b is vertical shift.
If |k|>1, then graph stretch vertically if 0<|k|<1, then graph compressed vertically. If k<0 or negative, then the graph reflected across x-axis.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
From (1) and (2) it is clear that
[tex]k=-3,a=-5,b=4[/tex]
k=-3<0, it means graph reflected across x-axis. |k|=3>1, so graph stretched vertically by factor 3.
a=-5<0, so the graph shifts 5 units right.
b=4>0, so the graph shifts 4 units up.
Therefore the reflected across x-axis, stretched vertically by factor 3 and shifted 5 units right and 4 units up.
