Chapter 2 Preview

Chapter 2 Preview

Let's review what you already know about quadratics

Absolute Value Equations

We solved these in chapter 2; let's make sure you have mastered these

Examples

• |5| = 5 because it is 5 units away from 0 on a number line

• |-3| = 3 because it is 3 units away from 0 on a number line

Multiple Select

|x+2| = 4

Choose all that apply

• -6

• 4

• -4

• 2

Multiple Select

3|x + 1|=21

Isolate the absolute value expression and set it equal to the other side as a positive and a negative.

x = ? Select all that appy

• -10

• -8

• 4

• 6

Solving Equations

Solving Absolute Value Equations doesn't change the fact that we need to isolate the variable

Note: a constant is a term that doesn't contain a variable. In 5x +2, the constant is 2 because it doesn't contain a variable. It is 'constantly' 2, unlike 5x which can change depending on the value of x.

Multiple Select

|-4 + x| = -4x + 6

Notice that the absolute value expression is isolated. The rule doesn't change just because there are x's on both sides of the equal sign. Set the absolute value expression equal to the positive and negative values of the other side. Select the 2 correct options.

• -4 + x = -4x + 6

• -4 + x = 4x + 6

• -4 + x = -4x - 6

• -4 + x = 4x - 6

Multiple Choice

First solve -4 + x = -4x + 6. You must move all the x's to one side of the equal sign and all the constants to the other. What is the result?

• -3x = 2

• 3x = -10

• -5x = -2

• 5x = 10

Multiple Choice

Divide both sides by 5 to solve x = 2.

But we have the 2nd equation to solve.

Solve -4 + x = 4x - 6. Move all of the x's to one side of the equal sign and the constants to the other. What is the result?

• -3x = 2

• -3x = -2

• 5x = -10

• 5x = -2

Multiple Choice

Divide both sides by -3 to solve  $x\ =\ \frac{2}{3}$  

Check both solutions; x = 2 and x = 2/3
Are they both correct, or is 1 solution extraneous? Select the correct response

• x = 2

•  $x\ =\ \frac{2}{3}$  

• x = 2  OR   $x\ =\ \frac{2}{3}$  

Combining Like Terms

• When adding and subtracting like terms, the exponents do not change

• Terms with like variables and exponents have their coefficients added/subtracted

Multiple Choice

 $2x^2\ +\ 3x^2\ -\ 2x\ +5x\ -\ 6\ +\ 11$  

Simplify

•  $5x^2-3x+5$  

•  $5x^2+8x+5$  

•  $5x^2+3x+5$  

•  $5x^2+7x+5$  

Multiple Choice

Simplify

 $-3x^2-4x-2x^2-12-2x-3$  

•  $-5x^2-2x-6$  

•  $-5x^2=2x-9$  

•  $-5x^2-2x-15$  

•  $-5x^2-6x-15$  

Multiple Choice

Solve for x without a calculator.

 $3+x^2-4x=x^2+7+8x$  

• 3

•  $\frac{1}{3}$  

• -3

•  $-\frac{1}{3}$  

Multiple Choice

We will use the quadratic formula in chapter 2. Which is the quadratic formula?

• $x=\frac{b+\sqrt{b-4ac}}{2}$

• $x=\frac{-b-\sqrt{b-4ac}}{2}$

• $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

• $x=-b\pm\frac{\sqrt{b^2-4ac}}{2a}$

Quadratic Formula

• Used to find x-intercepts of a parabola

• Useful in real-world scenarios, such as finding the time it takes for an object to reach the ground

• Order of Operations is very important when using the Quadratic Formula!

Time to practice plugging numbers into just part of the quadratic formula.

• Remember to plug in numbers in parentheses to avoid mistakes!

• 
  

• 
  

Multiple Choice

Simplify without a calculator. Use the following values of a, b, & c to find the value of the expression

 $b^2-4ac$  
a=3, b=2, c=-5

• 64

• -56

• -58

• 62

Multiple Choice

Simplify without a calculator. use the following values of a, b, & c to find the value of the expression $b^2-4ac$  

a=-2, b=-3, c=-4

• 23

  
  

• -41

• 41

• -23

Fill in the Blank

 $\left(-1.56^2\right)-3\left(-12.4\right)\left(3.2\right)$  

Simplify with a calculator. Do not round

You also have to simplify radicals when using the quadratic formula

Remember simplifying radicals with a factor tree!

Multiple Choice

 $\sqrt{48}$  

Simplify without a calculator

•  $3\sqrt{4}$  

•  $4\sqrt{3}$  

•  $2\sqrt{12}$  

•  $12\sqrt{2}$  

Multiple Choice

 $\sqrt{72}$  

Simplify without a calculator

•  $8\sqrt{3}$  

•  $3\sqrt{8}$  

•  $2\sqrt{6}$  

•  $6\sqrt{2}$  

Lots of factoring in chapter 2!!

We can factor rather than use the quadratic formula to find the x-intercepts of a parabola.

Multiple Select

What two numbers will both multiply to equal -50 and add to equal -5?

• -10

• 5

• 10

• -5

• 25

Multiple Select

What two numbers multiply to equal 42 and add to equal -13?

• 6

• -6

• 7

• -7

• 3

Multiple Select

What two numbers multiply to equal -48 and add to equal -8?

• 6

• -12

• 8

• -4

• 4

Multiple Choice

Factor

 $x^2+6x-27$  
Remember, you are looking for two numbers that multiply to -27 and add to 6

• (x-9)(x+3)

• (x-3)(x+9)

• (x+2)(x-3)

• (x-2)(x+3)

Hopefully you remember how to foil!

If you didn't take good notes from the video quiz, here are the steps again...

The opposite of factoring is FOILing

FOIL = First, Outer, Inner, Last

First: multiply the 1st term in each group

Outer: multiply the outside terms (first term of group 1 by second term of group 2)

Inner: multiply the inner terms (second term of group 1 by first term of group 2)

Last: multiply the last term in each group

Multiple Choice

Simplify (Hint: FOIL)
(x+5)(x-2)

•  $x^2-3x-10$  

•  $x^2+3x-10$  

•  $x^2-3x+10$  

•  $x^2+3x+10$  

Multiple Choice

Simplify

(2x-1)(5x+2)

• $10x^2-x-2$

• $10x^2-x+2$

• $10x^2+x-2$

• $10x^2+x+2$