Section 4.3- Modeling with Quadratic Functions

Essential Question: How can we model real-life situations using quadratic functions?

Hint: Write the equation in vertex form first! Solve for a.

Example 1: Writing an Equation of a Parabola (No Calculator)

What is the equation of a parabola containing the points

  • Substitute (x, y) values into
  • Write a system of equations.
  • Solve for values of a, b, and c by elimination.
  • Recall: c is the y-intercept of the quadratic function

a. Write system of equations.

b. Solve by elimination.

Example 2: Comparing Quadratic Models (Calculator)

Campers at an aerospace camp launch rockets on the last day of camp.

  • The path of Rocket 1 is modeled by the equation where tis time in second and h is the distance from the ground. Rocket 2
  • The path of rocket 2 is modeled by the graph at the right.

a. Which rocket flew higher? How much higher?

b. Which rocket stayed in the air longer? What were the times for each rocket?

c. What is the reasonable domain and range for each quadratic model?

d. Describe what the domains tell you about each of the models and why the domains for the models are different.

Example 3: Using Quadratic Regression (Calculator)

The table shows a meteorologist’s predicted temperatures for a summer day in Denver, Colorado.

a. What is a quadratic model for this data?

b. Predict the high temperature for the day.

c. At what time does the high temperature occur?


Use the 24-hour clock format to input times! / Using Quadratic Regression Function on Graphing Calculator
  • Use STAT feature on calculator
  • Click EDIT
  • Enter the x-values into L1; enter the y-values into L2
  • Go to STAT CALCQuadReg
  • Be sure that all values are showing especially the correlation coefficient (r)
  • If not, hit 2nd CATALOG (The 0 button); scroll down to Diagnostic On and press Enter twice

a. Quadratic Function

b. High temperature?

c. What time does the high temperature occur?

HW: p. 213 #20, 22-24 (No Calculator), 25, 26 (With Calculator)