A quadratic function, f(x) = x2 + bx + 9, is such that there is only one real root. Which of the following are possible values of b? I. b = 2
II. b = 6
III. b = -6
IV. b = -2

A. I, II, III, and IV
B. I and IV only
C. II and III only
D. I only

C

Step-by-step explanation:

Remember that we can use the discriminant to determine the amount of roots that a quadratic function has.

If the determinant equals 0, then we only have one real root.

Our function is given by:

Then the discriminant will be:

We only have one real root, thus our discriminant must be 0:

Solve for b:

Thus:

The answer is both II and III.

The final answer, then is C.

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.