To obtain the vertex of the function, compare the given equation to the following equation.
From the given, we obtain the following:
Substitute the obtained values to the vertex (h,k), where the values of h and k are as follows:
Thus, the vertex is at (4,6).
Since the variable x is raised to 2 and the value of a is negative, the parabola opens downwards.
Since the parabola opens downwards, the equation of symmetry is as follows.
Since the parabola opens downwards, the parabola has a maximum point at its vertex. Thus, f has a maximum of 6.
To obtain the x-intercepts, substitute 0 for f(x) and then solve for the value of x.
Thus, the x-intercepts are (1.55,0) and (6.45,0).
To obtain the y-intercept, substitute 0 for x and y for f(x). Then, solve for y.
Thus, the y-intercept is (0,-10).
To graph the equation, plot the vertex and the intercepts. Draw a smooth curve passing through the points from left to right.
Therefore, the graph of the quadratic function is shown below.