Question

draw the graph of the polynomial f(x)=x2-6x+9 ​

Answer 1

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Answer 2

The required graph is shown below:

Step-by-step explanation:

Consider the provided polynomial.

$f(x)=x^2-6x+9$

The provided equation is a quadratic equation.

Now compare the provided equation with standard equation $ax^2+bx+c$.

a=1, b=-6 and c=9

Since, the value of a is a positive number that means the graph of the equation is an upward parabola.

Substitute x=0 in above equation

$f(x)=0^2-6(0)+9$

$f(x)=9$

Substitute x=-1 in above equation

$f(x)=(-1)^2-6(-1)+9$

$f(x)=1+6+9$

$f(x)=16$

Substitute x=3 in above equation

$f(x)=(3)^2-6(3)+9$

$f(x)=9-18+9$

$f(x)=0$

Substitute x=6 in above equation

$f(x)=(6)^2-6(6)+9$

$f(x)=36-36+9$

$f(x)=9$

Now draw the graph using the table shown below:

 x        0     -1     3    6

f(x)       9     16    0    9

The required graph is shown below:

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