Heritage High School

Algebra 1

Week 5: 5/4-5/10

Included in this packet: Notes (These notes are to support your learning and for your reference. Notes will not be collected)

Intro to Solving Quadratics

Solving Quadratics Using Square Roots Notes Template Solving Quadratics Using Square Roots Notes Key

Solving Quadratics by Factoring Notes Template Solving Quadratics by Factoring Notes Key

You should treat these notes as if you were copying them down from the board – use the key to copy the notes onto your template (or if you don’t have a printer, you can just copy onto any paper that you have). While going through each problem, ask yourself if it makes sense or not, if you have questions, please view the lesson videos on my site, the tutorial videos in the Dynamic ebook on Clever or reach out to me!

Assignments to be submitted by 9:00 am on Monday, May 11:

Read p. 378-380 and p. 498-500 (hint: use the Dynamic e-book on Clever to see the video tutorials)

Complete Big Ideas – 7.5 p. 389 #32-36, 9.3 p. 501 #9-12, 17-21

Little to No Technology Access- You may take a pic/scan your assignment and email it to your Algebra 1 teacher or drop it off at the Main Administration office. Access to Technology- Please see directions on “Accessing Big Ideas Through Clever.” The preferred method to complete your homework is electronically through Clever.

Intro Notes:

Solving Quadratic Equations (Parabolas) – What are solutions? *We use many different names – roots, zeros, solutions, x-intercepts *Solutions are the values of x for a given y-value (usually when y=0 or when equation is re-written so that it equals zero)

Finding solutions answers these types of questions:

How long until ball hits the ground? How many tutoring packages are sold when profit is $0?

Solution: 4 seconds (it’s also on the ground at 0 seconds) O and 200 packages (blurry, but those are the x-int)

When does the golf ball have a height of 0 feet? How far does Mario jump?

Solution: 0 seconds and a little over 6 seconds

Additional reminders:

�2516

= √25√16

= 54 5 ± 3 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 5 + 3 & 5 − 3 5±3

2 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 5+3

2 & 5−3

2

8 & 2 4 & 1

Solve Quadratics by Factoring Name: _________________________________ Date: _________________________________

Examples: Find the solutions to the quadratic equations.

1) 4𝑔 − 40𝑔 2) 𝑦 − 4𝑦 − 12 3) 𝑥 − 9 You Try!

1) 4𝑥 − 9 2) 5𝑧 + 45𝑧 3) 𝑛 − 10𝑛 + 9

To find the solutions to a quadratic equation, factor the equation, then use the Zero Product Property to find the roots.

Zero Product Property If the product of two quantities equals zero, then at least one of the quantities equals zero.

If (𝑎)(𝑏) = 0, 𝑡ℎ𝑒𝑛 𝑎 = 0 𝑜𝑟 𝑏 = 0 Example: Find the roots of 2𝑥 − 8𝑥 2𝑥(𝑥 − 4) Factor

2𝑥(𝑥 − 4) = 0 Set the equation equal to zero 2𝑥 = 0 𝑜𝑟 𝑥 − 4 = 0 Use the Zero Product Property to solve for x

= 𝑜𝑟 + 4 + 4

𝑥 = 0 𝑜𝑟 𝑥 = 4 The solutions are called the roots and are the x-intercepts of the equation.

Simplifying Square Roots Name: Date:

Simplifying the √96:

=

=

= 2 ⋅ 2

= 4 Ex 1: √75 Ex 2: -3√54 Ex 3: √24𝑥𝑥5

You Try: 1: √24 2: 2√49𝑥𝑥3

96 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3

2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3

2 ⋅ 3

Simplifying Square Roots:

• Factor the radicand to it’s prime factors. (hint: use a factor tree) • Every group of 2 factors is replaced by one factor outside of the

radical. • Extra factors are left inside the radical. • Multiply all outside numbers together. Multiply all remaining

factors inside the radical together.

Solving Using Square Roots Name: Date:

Solve. Ex 1: 𝑥𝑥2 − 10 = −10 Ex 2: −5𝑥𝑥2 + 11 = 16 Ex 3: (𝑥𝑥 + 1)2 = 25 Ex 4: 𝑥𝑥2 − 13 = 15 You Try. 1: −3𝑥𝑥2 = −27 2: 𝑥𝑥2 + 7 = 19

Solve 𝑎𝑎𝑥𝑥2 + 𝑐𝑐 = 0 Using Square Roots • If a quadratic is written in the form 𝑎𝑎𝑥𝑥2 + 𝑐𝑐 =

0 you can solve using square roots • First, isolate the 𝑥𝑥2 on one side of the

equation • Then, solve by taking the square root of each

side • Remember, if you can’t square root evenly,

try to simplify the square root

Solve 𝟑𝟑𝒙𝒙𝟐𝟐 − 𝟐𝟐𝟐𝟐 = 𝟎𝟎 3𝑥𝑥2 − 27 = 0 +27 +27

3𝑥𝑥2

3=

273

𝑥𝑥2 = 9 √𝑥𝑥2 = √9 𝑥𝑥 = ±3

Isolate the 𝑥𝑥2 on one side of the equation

Square root both sides