Do Now Pass out the calcs.. Work on Practice EOC Week # 13 Block 4 ONLY: Pick up a homework answer...

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Transcript of Do Now Pass out the calcs.. Work on Practice EOC Week # 13 Block 4 ONLY: Pick up a homework answer...
Do Now
• Pass out the calcs..• Work on Practice EOC Week # 13 • Block 4 ONLY: Pick up a homework answer key
from the back table and correct your homework.
• Do yo thang...
Do Now
• Pass out the calcs..• Pick a homework answer from the table and
correct your homework form last night. • Solve the following problem by completing the
square. 4y2 + 4y  7 = 0
• Do yo thing...
Answer: 1.91, 0.91
Do Now• Pass out the calcs..• Hand your advertisement activity into the tray.• Work out the following TCAP question on a sheet of notebook paper.
Write an explanation next to EACH answer as to why or not you chose that answer.
Objective:
• So solve quadratic equations using the
QUADRATIC FORMULA!
Quadratic Formula
• To use this formula your equation must be in this form… ax2 + bx + c
Quadratic Formula
The FUN song…
• http://spongebob.nick.com/videos/clip/promospongebashfunsong.html
EXAMPLE 1 Standardized Test Practice
What are the solutions of 3x2 + 5x = 8?
–1 and – A 83
B –1 and 83 C 1 and – 8
3 D 1 and 83
SOLUTION
Write original equation.3x2 + 5x = 8
Write in standard form.3x2 + 5x – 8 = 0
Quadratic formula ±x = –b b2 – 4ac2a
EXAMPLE 1 Standardized Test Practice
Substitute values in the
quadratic formula: a = 3, b = 5,
and c = –8.
Simplify.= –5± 1216
Simplify the square root.= –5 ± 116
The solutions of the equation are –5 + 116 = 1 and
–5 – 116
= – 83
The correct answer is C. ANSWER
x = –5 ± 52 – 4(3)(–8)
2(3)
EXAMPLE 2 Solve a quadratic equation
2x2 – 7 = x
2x2 – x – 7 = 0
Solve 2x2 – 7 = x.
Write original equation.
Write in standard form.
Quadratic formulax =
b2 – 4ac+ ––b2a
Substitute values in the quadratic formula: a = 2, b = –1, and c = –7.
Simplify.
– (–1) –+ ( –1)2 – 4(2)(–7)
2(2)=
4=+ –1 57
EXAMPLE 2 Solve a quadratic equation
Write the equation in standard form, 2x2 – x – 7 = 0. Then graph the related function y = 2x2 – x – 7. The xintercepts are about –1.6 and 2.1. So, each solution checks.
ANSWER
1 + 57 2.14 and 1 – 4
–1.64.4
The solutions are
CHECK
57
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
EXAMPLE 3 Use the quadratic formula
y = 10x2 – 94x + 3900
4200 = 10x2 – 94x – 3900
0 = 10x2 – 94x – 300
Write function.
Substitute 4200 for y.
Write in standard form.
SOLUTION
For the period 1971 2001, the number y of films produced in the world can be modeled by the function y = 10x2 94x + 3900 where x is the number of years since 1971. In what year were 4200 films produced?
FILM PRODUCTION
EXAMPLE 3 Use the quadratic formula
Substitute values in the quadratic formula: a = 10, b = –94, and c = –300.
20,83694 + –20
= Simplify.
The solutions of the equation are:
ANSWER There were 4200 films produced about 12 years after 1971, or in 1983.
x = (–94)2 – 4 (10)(–300)–(–94)
+ –2(10)
94 + 20,836
2012 94 – 20,836
20–3.and
Methods for Solving the Quadratic Formula…
• Pg. 673
EXAMPLE 4 Choose a solution method
Tell what method you would use to solve the quadraticequation. 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.
Choose a solution methodEXAMPLE 4
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.
Tell what method you would use to solve the quadraticequation. Explain your choice(s).
b. x2 + 4x = 0
SOLUTION
Choose a solution methodEXAMPLE 4
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.
Tell what method you would use to solve the quadraticequation. Explain your choice(s).
c. 5x2 + 9x – 4 = 0
SOLUTION
GUIDED PRACTICE for Example 4
Tell what method you would use to solve the quadraticequation. Explain your choice(s).
SOLUTION
Factoring because the expression factors easily.
5. x2 + x – 6 = 0
GUIDED PRACTICE for Example 4
Tell what method you would use to solve the quadraticequation. Explain your choice(s).
SOLUTION
Factoring because the expression factors easily. Using square roots is another option since the equation can be written in the form x2 = d.
6. x2 – 9 = 0
GUIDED PRACTICE for Example 4
Tell what method you would use to solve the quadraticequation. Explain your choice(s).
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.
7. x2 + 6x = 5
Exit Ticket:
What are the solutions to the following equations? 1.2x2 + 7x = 9 2.3x2 – 1 = x
How can you choose which method to you use finding the roots to an equation?