1/9 - EMHS Math 1 EOC Review Blitz Day 1 (Quadrartics)

Math 1 EOC Review Blitz

Day 1: Quadratic Expressions

Operations With Quadratic Expressions

Addition: Combine like terms. Re-write in descending order

Subtraction: Distribute Negative (Change to +, then Add)

Multiplication: Use a Diagram (i.e. Box Method)

Subject | Subject

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Multiple Choice

Mild: Which expression is equivalent to $$\left(x+2\right)\left(3x-3\right)$$ ? NO CALCULATOR

• $$3x^2-6$$

• $$3x^2+3x-6$$

• $$3x^2+6x-6$$

• $$3x^2+9x-6$$

Multiple Choice

Medium: The perimeter of the triangle shown is $$8x-6$$ .

Which expression represents the length of QR? Calculator OK

• 4x-4

• 4x-6

• 6x-4

• 6x-8

Multiple Choice

Spicy: A rectangle has a perimeter of 64.

-Let x equal the width of the rectangle

-Let y equal the area of the rectangle

Which equation could be used to find the area of the rectangle?

• $$y=x^2-64x$$

• $$y=-x^2+64x$$

• $$y=x^2-32x$$

• $$y=-x^2+32$$

Multiple Choice

Spicy: David has a rectangle and a right triangle.

• The length of the rectangle is 5 more than its width, w.

• The length of the shorter leg of the triangle is equal to the rectangle’s width.

• The length of the longer leg of the triangle is twice the length of the rectangle.

Which function, f(w), represents the combined area of the rectangle and the triangle? (Hint: Recall that $$A_{Triangle}=\frac{1}{2}bh$$ ) Calculator OK

• $$f\left(w\right)=2w^2+10w$$

• $$f\left(w\right)=3w^2+15w$$

• $$f\left(w\right)=w^2+10w+25$$

• $$f\left(w\right)=w^2+15w+50$$

Example: -4x²+14x-6

-2(2x²-7x+3)

-2(2x+1)(x+3)

Step

1.) Factor out GCF

2.) Draw Box and fill in x² & constant

3.) Find factors of x² term and constant that correctly add to x terms

Factoring Quadratics

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Multiple Choice

Mild: Factor p² - 14p

• p(1 - 14)

• 2p(p - 7)

• p²(1-14)

• p(p - 14)

Multiple Choice

Mild: Factor 25x² - 81

• (5x - 9)(5x + 9)

• (5x - 9)(5x - 9)

• (5x + 9)(5x + 9)

• Cannot be factored

Multiple Choice

Medium: Factor k² -2k - 24

• (k+4)(k-6)

• (k+4)(k+6)

• (k+6)(k-1)

• (k-4)(k+6)

Multiple Choice

Spicy: Factor 3x² + 5x - 12

• (3x + 4)(x-3)

• (3x - 4)(x + 3)

• (3x + 3)(x -4)

• (3x - 3)(x + 4)

Multiple Choice

Spicy: Factor 3x² + 18x +15

• 3(x² + 6x + 5)

• (x + 5)(x + 1)

• 3(x + 5)(x + 1)

• Prime

1.) Set equation equal to zero

2.) Re-write expression in factored form using a diagram

3.) Set factors equal to zero and solve w/ zero-product property

Without a Calculator

1.) Set equation equal to zero

2.) Graph isolated expression

3.) Solutions are the x-intercepts of the graph

With a Calculator

Solving Quadratic Equations:

x²-4x+4=9

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Fill in the Blanks

Mild: What is the value of the positive zero defined by the function $f\left(x\right)=x^2-121$ ? No Calculator

Enter the numeric value only; do not type x= or any other characters

Multiple Choice

Medium: What are the solutions to the equation $$4x^2-52x+169=121$$ ? Calculator Active

• {1, -12}

• {-1, 12}

• {-1, -12}

• {1, 12}

Fill in the Blanks

Spicy: What is the value of the smaller zero of the function $f\left(x\right)=2x^2-8x-24$ ? No Calculator

Enter the numeric value only; do not type x= or any other characters

Key Features of Quadratic Functions

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x-intercepts: Intersect horizontal axis (solve f(x)=0)

y-intercept: Intersect vertical axis (plug in f(0))

Vertex: Maximum or minimum (find halfway b/n x-ints, then plug in x to find the y-value)

Multiple Choice

Mild: Which graph shows $$y=\left(4-x\right)\left(x+2\right)$$ ? No Calculator

Fill in the Blanks

Medium: A company models its net income, in thousands of dollars, with the function $f\left(x\right)=9x^2-54x-144$ , where x is the number of units of its product sold. How many units of its product does the company need to sell in order for the net income to equal $0? No calculator

Enter the numeric value only, do not type x= or any other characters