GOZUNTA
Try it now
Problem preview
A-CED.1 Warmup M2-002-A06-V04

Create and solve one-variable equations and inequalities, including absolute-value, linear, quadratic, simple rational, and exponential cases.

Create and solve a quadratic equation from motion context

Problem

At \(t\) seconds after launch, an object's height is \(h(t)~=~-2t^{2}~+~12t~+~5\). Use the displayed graph to set the height equal to \(15\), solve for \(\text{both}~\text{roots}\), and identify the time when the object is at that height on the way down.

A scaled graph of h of t equals negative two t squared plus twelve t plus five from zero through six seconds. The parabola begins at height five, reaches height twenty-three at three seconds, and crosses the height-fifteen target once while rising and once while descending. The intersection times are not annotated.
The motion model and height-15 target are shown on scaled axes without labeled intersections.
Open full size
Inside Gozunta

Turn the preview into practice.

More than a preview

Gozunta lets you study this problem—and more than 10,000 others.

Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.

Discover Gozunta Try it now
Four variants of this problem type
Curriculum context
Course
Math II
Standard
A-CED.1
Category
Algebra
Domain
Creating Equations
Objective
Create and solve one-variable equations and inequalities, including absolute-value, linear, quadratic, simple rational, and exponential cases.
Problem type
Create and solve a quadratic equation from motion context