Answer:
Option A. (4,0) and (-1,0)
Step-by-step explanation:
we know that
The equation of a vertical parabola in factored form is equal to
[tex]f(x)=a(x-x_1)(x-x_2)[/tex]
where
a is a coefficient
x_1 and x_2 are the zeros or x-intercepts of the function
In this problem we have
[tex]g(x)=-2(x-4)(x+1)[/tex]
we have
[tex]a=-2[/tex]
The leading coefficient is negative, that means the parabola open downward
The zeros of the function are
[tex]x_1=4\\x_2=-1[/tex]
Remember that the x-intercepts are the values of x when the value of the function is equal to zero
therefore
The x-intercepts are (4,0) and (-1,0)
