In the $xy$-plane, a parabola has vertex $(9,-14)$ and intersects the $x$-axis at two points. If the equation of the parabola is written in the form $\bm{y}=a\bm{x}^{2}+b\bm{x}+\bm{c}$, where $\bm{a}$, $\bm{b}$, and $\bm{c}$ are constants, which of the following could be the value of $\bm{a}+\bm{b}+\bm{c}$?

MM

Mashaal Masha

Feb 21, 2024

In the $xy$-plane, a parabola has vertex $(9,-14)$ and intersects the $x$-axis at two points. If the equation of the parabola is written in the form $\bm{y}=a\bm{x}^{2}+b\bm{x}+\bm{c}$, where $\bm{a}$, $\bm{b}$, and $\bm{c}$ are constants, which of the following could be the value of $\bm{a}+\bm{b}+\bm{c}$?

Difficulty: Hard

A:

$-$23

B:

$-$19

C:

$-$14

D:

$-$12

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ID: 65d62efc7c9dd71aa1ef615d