# SAT Math Multiple Choice Question 687: Answer and Explanation

Home > SAT Test > SAT Math Multiple Choice Practice Tests

### Test Information

- Use your browser's back button to return to your test results.
- Do more SAT Math Multiple Choice Practice Tests.

**Question: 687**

**12.**

A portion of the graph of the quadratic function *y* = *f*(*x*) is shown in the *xy*-plane above. The function *g* is defined by the equation *g*(*x*) = *f*(*x*) + *b*. If the equation *g*(*x*) = 0 has exactly one solution, what is the value of *b*?

- A. -2
- B. -1
- C. 1
- D. 2

**Correct Answer:** D

**Explanation:**

**D**

**Advanced Mathematics (transformations) HARD**

The graph of *y* = *g*(*x*) = *f*(*x*) + *b* is the graph of *f* vertically shifted up by *b* units. If *g*(*x*) = 0 has exactly one solution, the graph of *y* = *g*(*x*) can touch the *x*-axis at only one point: the vertex. Since the vertex of *f* has a *y*-coordinate of -2, this can only happen if *f* is shifted up 2 units, so *b* = 2.