Question

please remember to submit your workbook. examine the graph. © 2019 strongmind. created using geogebra. the motion of a rocket launched from the ground on an unnamed planet is shown on the given graph, where height (h) is a function of time (t). what is the equation for this model? select all that apply. h = -2t² - 4t + 48 h = t² - 2t + 24 h = t² + 2t - 24 h = 2t² + 4t - 48

Explanation:

Step1: Analyze the shape of the graph

The graph of the rocket's height - time function is a parabola opening downwards. The general form of a quadratic function is $h(t)=at^{2}+bt + c$, and for a parabola opening downwards, $a<0$.

Step2: Check each option

• Option 1: For $h=-2t^{2}-4t + 48$, where $a=-2<0$, $b=-4$, $c = 48$.
• Option 2: For $h=t^{2}-2t + 24$, $a = 1>0$, so this option is not correct as the parabola should open downwards.
• Option 3: For $h=t^{2}+2t-24$, $a = 1>0$, so this option is not correct as the parabola should open downwards.
• Option 4: For $h=2t^{2}+4t-48$, $a = 2>0$, so this option is not correct as the parabola should open downwards.

Answer:

$h=-2t^{2}-4t + 48$