# SAT Math Multiple Choice Practice Question 460: Answer and Explanation

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**Question: 460**

**1.**

The graph of *y* = *g*(*x*) is shown in the figure above. If *g*(*x*) = *ax*^{2} + *bx* + *c* for constants *a*, *b*, and *c*, and if *abc* ≠ 0, then which of the following must be true?

A. *ac* > 1

B. *c* > 1

C. *ac* < 0

D. *a* > 0

E. *ac* > 0

**Correct Answer:** E

**Explanation:**

**E** Remember your transformation rules. Whenever a parabola faces down, the quadratic equation has a negative sign in front of it. It always helps to plug in! Let's take an example. If your original equation was (*x* + 2)^{2}, putting a negative sign in front, –(*x* + 2)^{2}, would flip the parabola. If you expand out that equation, you get –*x*^{2} – 4*x* – 4. Notice that *a* in this equation is –1. Also, notice that *c* in the equation is just the *y*-intercept, because if you plug in 0 for *x* you get *y* = *c*. On the graph, the *y*-intercept is negative. And a negative number times a negative number is always positive. Again, plug in if you like it better: (–1)(–4) = +4. The best answer is E.