1. Get out Homework 9-6 Practice B Answers -13.10, 6.10 -2.15, 2.48
Lesson 9.6 Solve Quadratic Equations by the Quadratic Formula
Essential Question: How do you solve quadratic equations by
using the quadratic formula? Day 3
Date:
Warm-up:
CC.9.12.A.REI.4b
Solve quadratic
equations by
inspection, by
taking square roots,
completing the
square, the quadratic
formula and factoring,
as appropriate to the
initial form of the
equation. Recognize
when the quadratic
formula gives complex
solutions.
Get out Homework 9-6 Practice B
Answers
-13.10, 6.10
-2.15, 2.48
-1.82, 2.07
-3.73, -0.27
-3, 4
-2.61, 1.28
-4.61, -1.39
-13.44, 7.44
-2.11, 2.36
-1.45, 1.25
-3/2, 1/3
no solution

3. Standardized Test Practice
EXAMPLE 1
Standardized Test Practice
What are the solutions of 3x2 + 5x = 8?
–1 and – A 8 3 B
–1 and 8 3 C
1 and – 8 3 D
1 and 8 3
SOLUTION
3x2 + 5x = 8
Write original equation.
3x2 + 5x – 8 = 0
Write in standard form.
x = –b
b2 – 4ac 2a
Quadratic formula

4. Standardized Test Practice
EXAMPLE 1
Standardized Test Practice
Substitute values in the quadratic formula: a = 3, b = 5, and c = –8.
x = –5
52 – 4(3)(–8)
2(3) = –5
121 6
Simplify. =
–5 ± 11 6
Simplify the square root.
The solutions of the equation are
–5 + 11 6
= 1
and
–5 – 11 = – 8 3
The correct answer is C.
ANSWER

5. Solve a quadratic equation
EXAMPLE 2
Solve a quadratic equation
Solve 2x2 – 7 = x.
2x2 – 7 = x
Write original equation.
2x2 – x – 7 = 0
Write in standard form.
x =
b2 – 4ac + – –b 2a
Quadratic formula
Substitute values in the quadratic formula: a = 2, b = –1, and c = –7.
– (–1) – +
( –1)2 – 4(2)(–7)
2(2) = 4 = + –
Simplify.

6. EXAMPLE 2
Solve a quadratic equation
ANSWER
The solutions are 57 57
1 +
1 –
2.14 and
–1.64. 4 4
CHECK
Write the equation in standard form, 2x2 – x – 7 = 0. Then graph the related function y = 2x2 – x – 7. The x-intercepts are about –1.6 and 2.1. So, each solution checks.

7. GUIDED PRACTICE
for Examples 1and 2
Solve the equation by Quadratic Formula.
1. x2 – 8x + 16 = 0
ANSWER 4
2. 3n2 – 5n = –1
ANSWER
0.23, 1.43
3. 4z2 = 7z + 2
ANSWER
0.25, 2

8. Use the quadratic formula
EXAMPLE 3
Use the quadratic formula
For the period 1971  2001, the number y of films produced in the world can be modeled by the function y = 10x2  94x where x is the number of years since In what year were 4200 films produced?
FILM PRODUCTION
SOLUTION
y = 10x2 – 94x
Write function.
4200 = 10x2 – 94x – 3900
Substitute 4200 for y.
0 = 10x2 – 94x – 300
Write in standard form.

9. Use the quadratic formula
EXAMPLE 3
Use the quadratic formula
x =
(–94)2 – 4 (10)(–300)
–(–94) + –
2(10)
Substitute values in the quadratic formula:
a = 10, b = –94, and c = –300.
20,836 94 + – 20 =
Simplify.
The solutions of the equation are:
94 +
20,836 20 12
94 –
–3.
and
ANSWER
There were 4200 films produced about 12 years after 1971, or in 1983.

10. GUIDED PRACTICE
for Example 3 4.
WHAT IF? In Example 3, find the year when 4750 films were produced.
ANSWER
1986

11. To find:

12. EXAMPLE 4
Choose a solution method
Tell what method you would use to solve the quadratic
equation. Explain your choice(s).
a. 10x2 – 7 = 0
SOLUTION
a. The quadratic equation can be solved using square
roots because the equation can be written in the form
x2 = d.

13. EXAMPLE 4
Choose a solution method
Tell what method you would use to solve the quadratic
equation. Explain your choice(s).
b. x2 + 4x = 0
SOLUTION
b. The equation can be solved by factoring because the
expression x2 + 4x can be factored easily. Also, the
equation can be solved by completing the square
because the equation is of the form ax2 + bx + c = 0
where a = 1 and b is an even number.

14. EXAMPLE 4
Choose a solution method
Tell what method you would use to solve the quadratic
equation. Explain your choice(s).
c. 5x2 + 9x – 4 = 0
SOLUTION
c. The quadratic equation cannot be factored easily,
and completing the square will result in many
fractions. So, the equation can be solved using the
quadratic formula.

15. GUIDED PRACTICE
for Example 4
Tell what method you would use to solve the quadratic
equation. Explain your choice(s).
5. x2 + x – 6 = 0
SOLUTION
Factoring because the expression factors easily.

16. GUIDED PRACTICE
for Example 4
Tell what method you would use to solve the quadratic
equation. Explain your choice(s).
6. x2 – 9 = 0
SOLUTION
Factoring because the expression factors easily. Using square roots is another option since the equation can be written in the form x2 = d.

17. GUIDED PRACTICE
for Example 4
Tell what method you would use to solve the quadratic
equation. Explain your choice(s).
7. x2 + 6x = 5
SOLUTION
Completing the square because the equation is of the form ax2 + bx = c where a = 1 and b is an even number. Another method is the quadratic formula since the equation does not factor easily.

18. Classwork/Homework
9.6 Practice B Finish all!