Kindly check below
1) Let's do it in parts.
a) We can find the x-intercepts by using the factor zero property from each factor. Like this:
[tex]\begin{gathered} -(x+4)=0\Rightarrow-x-4=0\Rightarrow-x=4\Rightarrow x=-4 \\ (x-1)=0\Rightarrow x=1 \end{gathered}[/tex]
The best way to find the y-intercept with this factored form is by plugging into that equation x=0
[tex]\begin{gathered} f(x)=-\left(x+4\right)\left(x-1\right) \\ y=-\left(x+4\right)\left(x-1\right) \\ y=-(0+4)(0-1) \\ y=-(4)(-1) \\ y=4 \end{gathered}[/tex]
b) Expanding those factors by distributing them (FOIL) we can find this:
[tex]\begin{gathered} f(x)=-\left(x+4\right)\left(x-1\right) \\ f(x)=-\left(xx+x\left(-1\right)+4x+4\left(-1\right)\right) \\ f(x)=-x^2-3x+4 \end{gathered}[/tex]
So now, let's find the x-coordinate of the vertex V(h,k):
[tex]\begin{gathered} h=\frac{-b}{2a}=\frac{-(-3)}{2(-1)}=\frac{3}{-2}=-\frac{3}{2} \\ Axis\:of\:symmetry:x=-3/2 \end{gathered}[/tex]
c) The coordinates of the vertex can be found by plugging the x-coordinate into the quadratic function. This way:
[tex]\begin{gathered} f(x)=-\left(x+4\right)\left(x-1\right) \\ f(-\frac{3}{2})=-(-\frac{3}{2}+4)(-\frac{3}{2}-1)=\frac{25}{4} \\ \\ V(-\frac{3}{2},\frac{25}{4}) \end{gathered}[/tex]
d) Finally, we can plot that function by setting a table:
So plotting these points (-2,6),(-1,6), (0,4), (1,0),(2,-6) and opening down the parabola for a is -1 we can plot this:
