Which function has only one x-intercept at (−6, 0)?

There are several functions that will give us the answer above. A linear function that fits this specification is f(x) = x + 6 and a quadratic function that fits this specification would be f(x) = x^2 + 12x + 36.

To find the linear function, start with a basic slope (m) of 1 (you could use any slope to find this, but 1 will be the easiest) and your ordered pair. Next you can solve for the equation.

y = mx + b

0 = (1)(-6) + b

0 = -6 + b

6 = b

Then you can write the equation using your slope and intercept.

f(x) = x + 6

To find a quadratic with just one x intercept, we know that we must have a double root. All quadratics have 2 roots, so to have only one intercept means we must have a double at that point. This point would be the one above. To solve, we would need to use the term (x + 6) and square it. We pick this term because it satisfies the point above.

f(x) = (x + 6)(x + 6)

f(x) = x^2 + 6x + 6x + 36

f(x) = x^2 + 12x + 36

There are many others, but this is 2 of them.

The Right answer is D

Step-by-step explanation:

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