Answer:
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 <em>negative </em>1, so the parabola will <em>open downwards</em>.
<u>Axis of symmetry:</u> It is the line which will divide the parabola in two equal congruent halves.
Formula for axis of symmetry is:
It is shown as <em>dotted line </em>in the image attached in the answer area.
<em>Axis of symmetry will also contain the vertex of the parabola.</em>
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 <em>P(2, 16).</em>
Now, let us find points of parabola to sketch graph:
put x = 0,
Another point is <em>Y(0,12)</em>
Now, let us put y = 0, it will give us two points because the equation is quadratic in x.
So, other two points are <em>X1(-2, 0)</em> and <em>X2(6,0).</em>
If we plot the points P, Y, X1 and X2 we get a graph as attached in the image in answer area.