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**Hint:**In this question, we have to find out the type of the equation by the graphical representation.

For doing that first we need to consider the points \[x = 0,1,2,3\] putting this in the given equation and find out the coordinates (x,y) and plot in the graphs. Then we need to predict what the graph represents.

**Complete step by step answer:**

In this question we have to find out the type of the equation by the graphical representation.

The given equation is \[y = {x^2} - 3x - 4\].

Now we need to first graphically plot it, for doing that we need to find out the y coordinates for the x values \[x = 0,1,2,3\]…...

Now putting \[x = 0\]in the given equation we get,

\[y = - 4\]

putting \[x = 1\]in the given equation we get,

\[y = 1 - 3 - 4\]

Solving we get,

\[y = - 6\]

Now putting \[x = 2\]in the given equation we get,

\[y = {2^2} - 3 \times 2 - 4\]

\[y = 4 - 6 - 4 = - 6\]

Now putting \[x = 3\]in the given equation we get,

\[y = {3^2} - 3 \times 3 - 4\]

\[y = 9 - 9 - 4 = - 4\]

Putting \[y = 0\]in the given equation we get,

\[{x^2} - 3x - 4 = 0\]

Solving we get,

\[{x^2} - 4x + x - 4 = 0\]

\[x(x - 4) + 1(x - 4) = 0\]

\[(x - 4)(x + 1) = 0\]

\[x = 4or, - 1\]

Hence the points on the given equation are

\[(0, - 4),(1, - 6),(2, - 6),(3, - 4),(4,0),( - 1,0)\]

Hence Graph drawn from the equation \[y = {x^2} - 3x - 4\] will be a parabola.

**Note:**Parabola: A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line which is known as the directrix.

Coordinate: In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

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