Question

Which of the following is an x-intercept of the graph of the function shown below?
f(x)=x² + 6x +9

Answer 1

Answer: Second option.

Step-by-step explanation:

By defintion, a Quadratic function is a polynomial of degree 2 and it has the following form:

$f(x)=ax^2+bx+c$

Therefore, the function given is Quadratic. This is:

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

The steps to find the roots (or the x-intercepts) of the function, are:

1. You must substitute $f(x)=0$:

$0=x^2 + 6x +9$

2. Now, you can factor the Quadratic equation. Choose two numbers whose sum is 6 and whose product is 9. Notice that:

$3+3=6\\3*3=9$

Therefore,  you will get a "Double root".

4. So the solution is:

$(x+3)^2=0\\\\x=-3$

Answer 2

Answer:

B. x = -3

Step-by-step explanation:

To find the x-intercept, substitute 0 for y and solve for x.

x-intercept(s): (-3,0)