The table below presents the crude steel production in the USA, measured in millions of metric tons:| Year | Crude Steel Production ||------|-------------------------|| 1980 | 80 || 1985 | 90 || 1989 | 92 |**Task (A):** Determine a quadratic function $ f(x) = ax^2 + bx + c $ that models this data, where $ x $ represents the number of years since 1980.Given function form: \[ f(x) = \_\_\_ x^2 + 2.833x + 80 \]Your task is to find the coefficient for $ x^2 $.

Topic = Functionfx=ax2+bx+cform the given table dataIn the year 1980 , x=0we getf0=a02+b0+cform the table f0=8080=0+0+cc=80In the year 1985 , x=5we getf5=a52+b5+80form the table f5=9090=25a+5b+8025a+5b=105a+b=2b=2-5a ...............eq1In the year 1989 , x=9we getf9=a92+b9+80form the table f9=9292=81a+9b+8081a+9b=1227a+3b=4 ................eq2form the eq1 , b=2-5aput in eq227a+32-5a=427a+6-15a=412a=-2a=-16a=-0.1667then the quadratic function isf(x)=-0.1667x2+2.833x+80

Math

Algebra

The following table shows the crude steel production in the USA, in millions of Metric tons. Year Crude Steel Production 1980 0 1985 1989 59 80 90 92 ... (A) Find a quadratic function f(x) = ax² +bx+c that fits the data, where x represents the number of years after 1980. f(x)= x2 +2.833x+80.

The following table shows the crude steel production in the USA, in millions of Metric tons. Year Crude Steel Production 1980 0 1985 1989 59 80 90 92 ... (A) Find a quadratic function f(x) = ax² +bx+c that fits the data, where x represents the number of years after 1980. f(x)= x2 +2.833x+80.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

The table below presents the crude steel production in the USA, measured in millions of metric tons:

| Year | Crude Steel Production |
|------|-------------------------|
| 1980 | 80 |
| 1985 | 90 |
| 1989 | 92 |

**Task (A):** Determine a quadratic function $ f(x) = ax^2 + bx + c $ that models this data, where $ x $ represents the number of years since 1980.

Given function form:

\[ f(x) = \_\_\_ x^2 + 2.833x + 80 \]

Your task is to find the coefficient for $ x^2 $.

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