If $a, b$ and $c$ are positive, consecutive terms of a geometric sequence (that is, $\frac{c}{b}=\frac{b}{a}$ ), then the graph of $y=a x^{2}+b x+c$ is

(A) a curve that intersects the $x$-axis at two distinct points

(B) entirely below the $x$-axis

(C) entirely above the $x$-axis

(D) a straight line

(E) tangent to the $x$-axis

## Part C: Each correct answer is worth 8.
Since $a, b$ and $c$ are the consecutive terms of a geometric sequence, then $\frac{c}{b}=\frac{b}{a}$ or $b^{2}=a c$.

Therefore, the discriminant of the quadratic equation $a x^{2}+b x+c=0$ is $\Delta=b^{2}-4 a c=a c-4 a c=-3 a c<0$ since $a$ and $c$ are both positive.

Since the discriminant is negative, the parabola does not intersect the $x$-axis. Since the leading coefficient, $a$, is positive, then the parabola is entirely above the $x$-axis.

ANSWER: (C)