Answer
$$
y=-3x^{2}-6x+4
$$
The $x$-intercepts are
$$
x_{1}=-\frac{3+\sqrt{21}}{3}\approx -2.53 ,\:x_{2}=\frac{\sqrt{21}-3}{3} \approx 0.53
$$
The $y$-intercept is 4.
Vertex parabola is$\left(-1 , 7 \right)$.
The axis is $x=-1 $ , the vertical line through the vertex.
Plotting the vertex, the $y$-intercept,the $x$-intercepts. and the point $\left(-1 , 7 \right)$ gives the graph in Figure
Work Step by Step
$$
y=-3x^{2}-6x+4
$$
The $x$-intercepts can be found by letting $y=0$ to get
$$
y=-3x^{2}-6x+4=0
$$
This does not appear to factor, so we’ll try the quadratic formula.
$$
x_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\left(-3\right)4}}{2\left(-3\right)}
$$
from which
$$
x_{1}=-\frac{3+\sqrt{21}}{3}\approx -2.53 ,\:x_{2}=\frac{\sqrt{21}-3}{3} \approx 0.53
$$
are the $x$-intercepts.
Set $x=0 $ to find the $y$-intercept.
$$
y=-3(0)^{2}-6.(0)+4=4.
$$
So the $y$-intercept is 4.
The $x$-coordinate of the vertex is :
$$
x=\frac{-b}{2a}=\frac{6}{-6}=-1
$$
Substituting this into the equation gives
$$
y=-3(-1)^{2}-6(-1)+4=-3+6-4=7
$$
The vertex is $\left(-1 , 7 \right)$.
The axis is $x=-1 $ , the vertical line through the vertex.
Plotting the vertex, the $y$-intercept,the $x$-intercepts. and the point $\left(-1 , 7 \right)$ gives the graph in Figure