Question

1. which graph bests represents $f(x) = -x^2 + 2x + 3?$abcdclear my selection7multiple choice 8.3 points16) a toy rocket was launched from a 3 ft tall platform with an initial velosity of 55 ft/s. $f(t)$ is shown on the graph where $f$ is the height in feet and $t$ is time in seconds.height of toy rocket over time

Explanation:

Step1: Identify parabola direction

The coefficient of $x^2$ is $-1$ (negative), so the parabola opens downward. This eliminates options C and A (which open upward).

Step2: Find y-intercept

Set $x=0$: $f(0)=-(0)^2+2(0)+3=3$. The y-intercept is $(0,3)$.

Step3: Find vertex

Use vertex formula $x=-\frac{b}{2a}$. For $f(x)=-x^2+2x+3$, $a=-1$, $b=2$.
$x=-\frac{2}{2(-1)}=1$.
Calculate $f(1)=-(1)^2+2(1)+3=-1+2+3=4$. Vertex is $(1,4)$.

Step4: Match to graph

Option B has a downward-opening parabola, y-intercept at $(0,3)$, and vertex at $(1,4)$, which matches all properties.

Answer:

B. <The downward-opening parabola with y-intercept (0,3) and vertex (1,4)>