Question

the height in feet of the curved arch support for a bridge can be modeled by $f(x) = -0.0009x^2 + 1.24x + 1.65$. you are standing on a platform 2 feet above the maximum height of the arch. if you bungee from this point, and your bungee will stretch to 420 feet before retracting; are you safe to jump?
yes
no

Explanation:

Step1: Find x-coordinate of vertex

For quadratic $f(x)=ax^2+bx+c$, $x = -\frac{b}{2a}$
$x = -\frac{1.24}{2\times(-0.0009)} = \frac{1.24}{0.0018} \approx 688.89$

Step2: Calculate max arch height

Substitute $x\approx688.89$ into $f(x)$
$f(688.89) = -0.0009(688.89)^2 + 1.24(688.89) + 1.65$
$f(688.89) \approx -0.0009(474567.9) + 854.22 + 1.65$
$f(688.89) \approx -427.11 + 854.22 + 1.65 \approx 428.76$ feet

Step3: Find total jump height

Add 2 feet to max arch height
Total height $= 428.76 + 2 = 430.76$ feet

Step4: Compare to bungee stretch

$430.76 > 420$, so jump is unsafe.

Answer:

No