What are the Zeros of a Quadratic Function?

A teacher explaining quadratic functions to students, Cape Town, South Africa
BFG Images/Getty Images

The graph of a quadratic function is a parabola. A parabola can cross the x-axis once, twice, or never. These points of intersection are called x-intercepts or zeros.  

In your textbook, a quadratic function is full of x's and y's. This article focuses on the practical applications of quadratic functions. In the real world, the x's and y's are replaced with real measures of time, distance, and money. To avoid confusion, this article focuses on zeros and not x-intercepts.

Four Methods of Finding the Zeros

This article focuses on using a graph to identify the zeros. Before you begin this tutorial, make sure that you can confidently plot ordered pairs on a Cartesian Plane.

Two Zeros

Woman paying bills online at home
Portra Images/DigitalVision/Getty Images

Living from paycheck to paycheck is rough. Granted, you can't take it with you, but it's no fun commemorating the first and last of each month with a meal of Alpo and saltines.

Tired of this boom-to-bust cycle (and eating dog food), Teresa has decided to study her checking account balance over the course of a month.

Questions

  1. Where are the zeros on this graph?
  2. What do they mean?

Two Zeros - Answers

Empty Wallet
Adam Gault/Photographer's Choice RF/Getty Images

1. Where are the zeros on this graph?

The zeros are located at (0,0) and (30,0).

2. What do they mean?

(0,0):  At the beginning of the month, Teresa has $0 in her bank account.

(30,0): At the end of the month, Teresa has $0 in her bank account.

 

One Zero

Mother and daughter on Ferris wheel
Rebecca Nelson/Moment/Getty Images

At the carnival, revelers line up to ride the Ultra Cyclone Monster. After standing in line for an hour, Bianca and her cousins take their seats on the ride.

When the ride returns to the loading dock, a camera automatically captures the riders. Then the Monster hurtles the riders to the horizon.

Questions

  1. Where is the zero on this graph?
  2. What does it mean?

One Zero - Answers

Amusement park at night, Coney Island, NY
Rudi Von Briel/Photolibrary/Getty Images

1.  Where is the zero on this graph?

(5,0)

2.  What does it mean?

Passengers of the Ultra Cyclone Monster need to say "Cheese" when the ride hits its 5 second mark.

No Zeros

Gold Bangles For Sale In Gold Souk; Dubai, United Arab Emirates
Ian Cumming/Perspectives/Getty Images

Reza, a gold merchant, has noticed that gold prices resemble a quadratic function. 

Questions

  1. Where are the zeros of this function?
  2. What does it mean?

No Zeros - Answers

The gold souq, Dubai, UAE.
Katarina Premfors/arabianEYE/Getty Images

1. Where are the zeros of this function?

Nowhere

2. What does it mean?

Over the last 14 years, Reza has always charged more than $0 for the precious metal.

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Your Citation
Ledwith, Jennifer. "What are the Zeros of a Quadratic Function?" ThoughtCo, Dec. 7, 2017, thoughtco.com/zeros-of-a-quadratic-function-2311830. Ledwith, Jennifer. (2017, December 7). What are the Zeros of a Quadratic Function? Retrieved from https://www.thoughtco.com/zeros-of-a-quadratic-function-2311830 Ledwith, Jennifer. "What are the Zeros of a Quadratic Function?" ThoughtCo. https://www.thoughtco.com/zeros-of-a-quadratic-function-2311830 (accessed May 25, 2018).