Algebra 1 Common Core Student Edition, Grade 8-9

Co n cep t Byt e

Use W it h Lesson 9-3

Finding Roots

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

F-IF.C.7a Graph linear and quadratic functions and

show intercepts, maxima, and minima. A ls o A-REI.B.4

MP 5

The solutions of a quadratic equation are the x-intercepts of the graph of the related

quadratic function. Recall that the solutions and the related x-intercepts are often

called roots of the equation or zeros of the function.

Activity

Use a graphing calculator to solve x 2 - 6x + 3 = 0.

Step 1 Enter y = x2 - 6x + 3 on the Y= screen. Use the CALC feature. Select ZERO.

The calculator will graph the function.

Step 2 Step 3 Step 4

MATHEMATICAL

PRACTICES

\

1 Zer0

1 X = .55051026- Y = 0

Move the cursor to the

left of the first x-intercept.

Press ^552^ to set the left

bound.

Move the cursor slightly to

the right of the intercept.

Press to set the right

bound.

Press 4323^ to display the

first root, which is about

0.55.

Repeat Steps 2-4 for the second x-intercept. The second root is about 5.45. So the

solutions are about 0.55 and 5.45.

Suppose you cannot see both of the x-intercepts on

your graph. You can find the values of y that are close

to zero by using the TABLE feature. Use the TBLSET

feature to control how the table behaves. Set ATBL

to 0.5. Set INDPNT: and DEPEND: to AUTO. The

calculator screen at the right shows part of the table for

y = 2x2 - 48x + 285.

X Yi

10.5 11

11.5 12

12.5

13

BW i

(^1.5^

-2.5

<fc

The graph crosses the x-axis

when the values for y change

signs. So the range of x-values

should include 10.5 and 13.5.

1

X = 13. 5 V ~ 1 -------------'

Ex e r c i se s

Use a graphing calculator to solve each equation. Round your solutions to the

nearest hundredth.

1. x2- 6 x - 16 = 0


2. x2 — 18x + 5 = 0


3. 2x2 + x — 6 = 0


4. 0.25x2 - 8x - 45 = 0


5. |x2 + 8x - 3 = 0


6. 0.5x2 + 3x — 36 = 0

c

PowerAlgebra.com Co n c e p t B y t e Fi n d i n g Ro o t s 567