Algebra 1 Common Core Student Edition, Grade 8-9

Concept Byte

Use W it h Lesson 9-4

Writing Quadratic

Equations

Co m m o n Co r e St at e St a n d a r d s

A-CED.A.2 Create equations in tw o variables

to represent the relationships between quantities.

MP 2

In Lesson 9-2, you learned the standard form of a quadratic equation, ma t h ema t ic a l

ax2 + bx + c = 0. You have also learned how to find the roots of quadratic PRACTICES

equations, and how to find the zeros of the related function.

1

1. Write the quadratic equation x2 - 2x - 15 = 0 in factored form.

2. What are the roots of the equation?


3. Graph the quadratic function y = x2 - 2x - 15. What are the zeros of the
   function?


4. How are the roots of the equation x2 - 2x - 15 = 0 related to the zeros of the
   function y = x2 - 2x- 15?

Activity 2

5. The roots of a quadratic equation are -2 and 8. How can the roots be used to write
   a quadratic equation in factored form? What are the factors of the quadratic
   expression?


6. What is this equation in standard form?


7. What is the related quadratic function in standard form?


8. How do you know the zeros of this function without graphing?


9. Graph the function on a graphing calculator. How can you use the calculator to
   check that the graph has the zeros you found in Exercise 8?

Activity 3

^

10. The graph of a quadratic function is shown at the right. What are the zeros of the
    function?


11. Write a quadratic function with the zeros you found in Exercise 10.


12. Choose another point on the graph and test whether it satisfies the equation
    you wrote in Exercise 11.


13. How can you use a graphing calculator to check that the function is correct?
    Explain, and check your work by using a graphing calculator.

f H23S1SES1B3ESSBS1I Concept Byte Writing^1 Quadratic Equations □ 573

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