Question

Question 10(Multiple Choice Worth 1 points)(08.01 MC)Which of the following is the graph of f(x) = x2 - 5x + 4?

Answer 1

we have the function

`f\left(x\right)=x^2-5x+4`

This is a vertical parabola open upward

The vertex is a minimum

step 1

Find out the vertex

Complete the square

`\begin{gathered} f(x)=(x^2-5x)+4 \\ f(x)=(x^2-5x+2.5^2-2.5^2)+4 \\ f(x)=(x-2.5)^2-2.25 \end{gathered}`

The vertex is the point (2.5,-2.25)

step 2

Find out the y-intercept (value of f(x) when the value of x=0)

so

For x=0

`\begin{gathered} f(x)=0^2-5(0)+4 \\ f(x)=4 \end{gathered}`

The y-intercept is (0,4)

step 3

Find out the x-intercepts (values of x when the value of f(x)=0)

`x^2-5x+4=0`

Solve the quadratic equation

using the formula

a=1

b=-5

c=4

substitute in the formula

`x=(-(-5)(+-)√(-5^2-4(1)(4)))/(2(1))`
`x=(5(+-)+3)/(2)`

The values of x are

x=4 and x=1

therefore

the x-intercepts are (1,0) and (4,0)

therefore

the graph of the given equation is