Unit 6 Lesson 19

Unit 6, 7, & 8

Quadratic Characterisitcs

Parts of the quadratic

Y-Intercept, x-intercept, axis of symmetry, solution, maximum, minimum, domain, range, increase, decrease, vertex

Multiple Choice

Does this graph have a maximum or minimum value?

• maximum

• minimum

• neither

• both

Multiple Choice

What are the coordinates of the vertex, and is it a maximum or minimum?

• (-1, 4); Maximum

• (-1, 4); Minimum

• (4, -1); Maximum

• (4, -1); Minimum

Multiple Choice

What is the y-intercept?

• (2, 6)

• 4

• -1,5

• (5.5, 0)

Multiple Choice

What is the axis of symmetry?

• x = -3

• (-3, -5)

• -1 and -5

• y = 4

Multiple Choice

What is the axis of symmetry?

• 2

• 4

• x = 2

• y = 4

Multiple Choice

Using the graph of the quadratic function, identify the range.

• y < -6

• -2 < x < 10

• -∞ < x < ∞

• -6 ≤ y < ∞

Multiple Choice

Find the zeros.

• 0 and 4

• 0 and -4

• 0

• -4

Multiple Choice

Use the graph to determine the x-intercept(s).

• (1, 0)

• (0, 3), (0, 1)

• (3, 0), (1, 0)

• (0, -3)

Multiple Choice

What is the range of this function?

• x > -2

• x ≥ -2

• y ≥ -2

• y > -2

Multiple Choice

If the blue graph is

f(x) = x²

then the red must be...

• g(x) = x² - 5

• g(x) = x² + 5

• g(x) = (x - 5)²

• g(x) = (x + 5)²

Algebraically: x method, punnet square

Multiple Choice:

Graph it or work your way backwards

Factor Quadratics

Multiple Choice

Factor

k²+7x+10

• (k+2)(k+5)

• (k-2)(k-5)

• (k+10)(k+4)

• (k+2)(k-5)

Multiple Choice

Factor completely: 
3x² + 18x +15
Hint: Factor GCF first.

• 3(x² + 6x + 5)

• (x + 5)(x + 1)

• 3(x + 5)(x + 1)

• Prime

Multiple Choice

Factor:

$$3x^3+8x^2-15x-40$$

• $$\left(x^2-8\right)\left(3x+5\right)$$

• $$\left(3x-8\right)\left(x^2-5\right)$$

• $$\left(3x+8\right)\left(x^2-5\right)$$

• $$\left(x^2+8\right)\left(3x-5\right)$$

Multiple Choice

Factor:

10a⁴+16a+10a²

• 2a(5a³⁺8+5a)

• 2a⁴(5a+8a²+5a³)

• 2a⁴(10+16a+40a²)

• 3a³(5+8a+a²)

Multiple Choice

Factor $$4r^2\ -\ 49$$

• $$(2r+7)(2r-7)$$  

• $$(2r+7)^2$$  

• $$\left(2r\ -\ 7\right)^2$$  

• $$(2r\ +\ 24.5)\left(2r\ -\ 24.5\right)$$  

Multiple Choice

Factor $$m^2\ -\ 36$$

• $$(m+18)(m-18)$$  

• $$(m+6)^2$$  

• $$\left(m\ -\ 6\right)^2$$  

• $$(m\ +\ 6)\left(m\ -\ 6\right)$$  

Multiple Choice

Factor $$x^2\ -\ 25y^2$$  completely

• $$(x+12.5y)(x-12.5y)$$  

• $$(x+5y)(x-5y)$$  

• $$\left(x\ -\ 5y\right)^2$$  

• $$(x+5y)^2$$  

Operations with Polynomials

Add, subtract, & Multiply Polynomials

Adding and Subtracting Polynomials

• For addition just combine like terms

• For subtraction change the signs of every value in the parenthesis and just add.

  
  

Subtracting Polynomials

Multiple Choice

Add or Subtract to Simplify:

(4x²+ x) - (x²+ 2x)

• 3x² - x

• 4x² + 2x

• 3x² + 3x

• 3x² + 2x

Multiple Choice

Simplify each expression.
(6b³ + 6 - b⁴) - (8b³ - 6b⁴ + 2)

• 4b⁴ - 2b³ + 7

• 5b⁴ - 2b³ + 4

• b⁴ - 2b³ + 7

• 5b⁴ - 2b³ + 7

Multiple Choice

Add the polynomials.
(3x³ + 3x² – 4x + 5) + (x³ – 2x² + x – 4)

• 4x³ + 1x² – 3x + 1

• 2x³ + 1x² - 5x + 9

• 6x³ + 1x - 1x² - 3

• 3x⁵ +1x - 1x⁵ - 3x

Multiplying Polynomials

• Distribute any number in front of a ( ) to all numbers inside the ( )

• Use the FOIL method to multiply binomials.

• 
  

• 
  

Multiple Choice

Find the product:

(3r-4)(7r-5)

• 21r²-43r+20

• 21r+43r²+9

• 7r+12r

• r+2r

Multiple Choice

(4a + 2)(6a² − a + 2)

• 24a³ + 16a² + 6a + 4

• 24a³ + 8a² + 10a + 4

• 24a³ + 8a² + 6a + 4

• 24a³ - 8a² - 6a + 4

Multiple Choice

• 10x⁹

• 24x¹⁴

• 24x⁹

• 10x¹⁴

How could you describe the area of the shaded region in terms of the two rectangles?

What is the area of the big rectangle?

What is the area of the small rectangle?

​

​Some text here about the topic of discussion.

What do we know?

Multiple Choice

How would you describe the area of the shaded region in terms of the two rectangles?

• The shaded region is the total of the big rectangle.

• The shaded region is the sum of the big rectangle and the small rectangle.

• The shaded region is the difference between the big rectangle and the small rectangle.

• The shaded region is not related to the big or small rectangle.

Multiple Choice

What is the area of the big rectangle?

• 9x²-6xy+3y²

• 3x²+y²