Answer:
The number of y-intercept of g(x) is greater than y-intercept of f(x).
Step-by-step explanation:
The given functions are
[tex]f(x)=x^2[/tex] (parent function)
[tex]g(x)=(x-2)^2-3[/tex]
These are parabolic functions.
The standard form of parabolic functions is
[tex]f(x)=a(x-h)^2+k[/tex]
Where, a is scale factor and (h,k) is vertex of parabola.
If h>0, then graph of parent function shifts h units right and If h<0, then graph of parent function shifts h units left.
If k>0, then graph of parent function shifts k units upward and If k<0, then graph of parent function shifts k units downward.
Therefore the graph of f(x) shifts 2 units right and 3 units downward to get graph of g(x).
Using the standard form we can say that f(x) has vertex (0,0) and g(x) has vertex (2,-3).
SInce value a>0, therefore f(x) an g(x) are upward parabola.
Since the vertex of f(x) is origin, therefore f(x) has one y-intercept, i.e., (0,0).
Since the vertex of g(x) is (2,-3) and it is an upward parabola, therefore g(x) has two y-intercepts.
[tex]0=(x-2)^2-3[/tex]
[tex]x=0.268,3.732[/tex].
Therefore number of y-intercept of g(x) is greater than y-intercept of f(x).
