Sketch the graph for the following quadratic function.
it's ok if it's wrong. i just wanna see how the work done to do this

Please refer to the attached image for the graph of given function.

Step-by-step explanation:

Given the equation:

Let us rewrite by letting it equal to .

Now, we can see that it is a quadratic equation and it is known that a quadratic equation has a graph of parabola.

Let us compare the given equation with standard quadratic equation:

we get:

Coefficient of is negative 1, so the parabola will open downwards.

Axis of symmetry: It is the line which will divide the parabola in two equal congruent halves.

Formula for axis of symmetry is:

It is shown as dotted line in the image attached in the answer area.

Axis of symmetry will also contain the vertex of the parabola.

It is a downward parabola so vertex will be the highest point on this parabola.

Putting x = 2 in the equation of parabola:

So, vertex will be at P(2, 16).

Now, let us find points of parabola to sketch graph:

put x = 0,

Another point is Y(0,12)

Now, let us put y = 0, it will give us two points because the equation is quadratic in x.

So, other two points are X1(-2, 0) and X2(6,0).

If we plot the points P, Y, X1 and X2 we get a graph as attached in the image in answer area.