Which of the following is the graph of f(x) = x2 − 5x + 4?

 refer attachment for the graph.

Step-by-step explanation:

Given: The equation

We have to draw the the graph for the given equation.

Consider the given equation  

The vertex of the parabola of the form   is given by

Here, a = 1 , b = -5 and c = 4

Thus, vertex is

Also, the y coordinate at is

Simplify, we get,

Thus, The vertex of parabola is

y - intercept is the point where x = 0

Plug x = 0 in given equation

Thus, y - intercept is (0,4)

Now, we calculate x- intercept

x- intercept is where y is equal to 0.

Put f(x) = 0

We have,

Solving the given quadratic equation using quadratic formula ,we have

we have a = 1 , b = -5 and c = 4

Simplify, we have,

Thus,

Thus, The x - intercept are (4,0) and (0,1)

Plot the graph and we obtain as shown below.