Answer:
see the explanation
The graph in the attached figure
Step-by-step explanation:
we have
Function f(x)
[tex]f(x)=5x^{2}-3[/tex] ----> equation A
This is a vertical parabola open upward (because the leading coefficient is positive)
The vertex is a minimum
The vertex is the point (0,-3)
The y-intercept is the point (0,-3) [value of y when the value of x is equal to zero]
The x-intercepts are the points
[tex](-\sqrt{\frac{3}{5}},0)[/tex] and [tex](\sqrt{\frac{3}{5}},0)[/tex]
Function g(x)
[tex]g(x)=5x^{2}+3[/tex] ----> equation B
This is a vertical parabola open upward (because the leading coefficient is positive)
The vertex is a minimum
The vertex is the point (0,3)
The y-intercept is the point (0,3) [value of y when the value of x is equal to zero]
The function don't have x-intercepts (the roots are complex numbers)
We can say that the function g(x) is the translation of the function f(x) 6 units up
using a graphing tool
The graph in the attached figure
