GOZUNTA
Try it now
All courses Math II · F-IF.4 18 of 73
Interpret key graph/table features of quadratic models in context.

Interpret the vertex of a quadratic model in context

Problem
Interpret the vertex of h(t)=−16(t−2)²+70 feet models height at t seconds.
Your answer
With a free account

Try the session again.

Return to a past session and redo it when you want another look at the same skills.

Create a free account
With paid access

Separate understanding from one lucky answer.

Multiple variants of a problem type let you apply the method again before deciding that the skill is secure.

Compare plans

Hint

Label h with input units and k with output units before interpreting.

The vertex(h,k) pairs contextual input h with output k; sign(a) determines whether k is a maximum or minimum.

Solution walkthrough

01

Identify the model form

\[h(t)~=~-16(t-2)^2+70\]

This is a quadratic written in vertex form, so the key point is easy to read.

02

Read the vertex

\[(2,70)\]

The vertex says the important point happens at 2 seconds with a height of 70 feet.

03

Determine whether it is a maximum

\[-16<0\]

Because the coefficient is negative, the parabola opens downward, so the vertex is the highest point.

04

State the interpretation

\[\text{vertex}=(2,70);~\text{opening}=\text{down};~\text{extremum}~\text{type}=\text{maximum};~\text{contextual}~\text{input}=2~\text{seconds};~\text{contextual}~\text{output}=70~\text{feet};~\text{domain}~\text{status}=\text{vertex}~\text{occurs}~\text{after}~\text{launch};~\text{interpretation}=\text{model}~\text{predicts}~\text{peak}~\text{height}70\text{ft}~\text{at}2s\]

In the height context, the highest point of the parabola is the maximum height.

+

Another way

  1. Picture the graph as the path of a thrown object. The top of the path occurs at the vertex, so it gives the maximum height and when it happens.

!

Common mistake

A common mistake is to read 2 as the height and 70 as the time. In the ordered pair \((2,70)\), the first value is time and the second value is height.

Answer contextual quadratic graph or diagram labeling the requested feature, valid domain, units, and interpretation.
vertex=(2,70); opening=down; extremum type=maximum; contextual input=2 seconds; contextual output=70 feet; domain status=vertex occurs after launch; interpretation=model predicts peak height70ft at2s