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A-CED.1 Warmup M2-002-A06-V03

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 \(h(t)~=~-t^{2}~+~6t~+~7\). Use the displayed graph to set the height equal to \(0\), solve for \(\text{both}~\text{roots}\), and identify when the object hits the ground in the motion context.

A scaled graph of h of t equals negative t squared plus six t plus seven from negative one through seven seconds. The parabola meets height zero at the ends of the shown algebraic interval and reaches height sixteen at three seconds. The region before zero seconds is shaded as outside the motion context, and the roots are not annotated.
The motion model, ground target, and negative-time region are shown on scaled axes without labeled roots.
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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