Review for EOC Algebra

1) In the quadratic equation x² – x + c = 0, c represents an unknown constant. If x = -4 is oneof the solutions to this equation, what is the value of c?

(-4)² - (-4) + c = 0

16 + 4 + c = 0

c = -20

What is the other solution to the equation?0 = x² - x - 20

0 = (x - 5)(x + 4)

x = 5 and -4

2) What is the vertex and the roots of y = x² – 9?

“roots” of the equation are the x-intercepts…when y = 0

0 = x² - 9 can factor 0 = (x + 3)(x – 3)

Check the graph or the table:

Vertex (0, -9)

Roots are at

3 and -3 on x-axis

3) Given the function f(x) = -4x² - 6, what is the value of f(-3)?

What is the value of the function when x is -3?

f(-3) = -4(-3)² - 6

f(-3) = -42

f(-3) = -4•9 - 6f(-3) = -36 - 6

input

output

Or … put equation in Y = -4x - 6 ²And check the table

7(x – 1) – 4(x – 3) = 17

7x – 7 – 4x + 12 = 17 distribute

-5 -5 subtract 5 from both sides 3x + 5 = 17 combine like terms

3x = 12 3x = 12 divide both sides by 3 3

x = 4

4)

x + 6

x

5) The area of a rectangle is 16 square centimeters. The length is 6 more than the width. Set up and solve an equation to find the length of the rectangle

Area = length • width16 = (x + 6)•x Or … x² + 6x = 16

Quadratic Equation

1) FACTORING METHOD2) Quadratic Formula3) Graphing

x2 + 6x = 16 need to set the equation= 0, by moving 16 to other side

Gives you the: x-intercepts the roots of the equation the zeroes of the function

-16 -16x2 + 6x – 16 = 0 (x - 2)(x + 8) = 0 factor the trinomial

x - 2 = 0? x + 8 = 0? ask yourself what makes each factor = 0

x = 2 and x = -8 but for width, can not use the negative answer

The area of a rectangle is 16 square centimeters. The length is 6 more than the width. Set up and solve an equation to find the length of the rectangle

x + 6

x

Substitute x = 2 in for the length

The length is 8 cm

6) Solve the Equations:1) 4x + 16 = 20 Linear – subtract a 16 from both

sides, then divide by 4 on both sides

x = 1

Quadratic – already factored, readyto solve, what makes each factor = 0?

x = -½, and 5

Quadratic – needs to be factored

Pull out GCF 3x(x + 2) = 0Now figure what makes each factor = 0,

x = 0 and -2

2) (2x + 1)(x - 5) = 0

3) 3x2 + 6x = 0

7) What is the range of the function?

Smallest ………………….Largest

Is ‘range’ the x-values or the y-values?

yDoes the graph include -3? Yes ≤, No <

≤Does the graph include 4? Yes ≤, No <

≤-3 4

8) What is the domain of the function?

Smallest ………………….Largest

Is ‘domain’ the x-values or the y-values?

xDoes the graph include 0? Yes ≤, No <

<Does the graph include 6? Yes ≤, No <

≤ 60

9)Use the quadratic formula to solve for the zeroes of the function:

Y = 2x – 4x – 10 ²

Identify: a= ____ b = _____ c = ______2 -4 -10

Fill in the formula:

Y = 2x – 4x – 10 ²

Simplify: 4 ±√964

Put in calculator to get both answers:

__________ and __________ 3.45 -1.45

Find the vertex of this parabola: ( , ) 1 -12

10) Identify each of the following from the graph:a) The line of symmetry

___________

b) The zeroes of the function ___________

c) The vertex ___________

d) The number of real roots _______

e) The parent function: ___________

x = 2

-1 and 5

y = x²2

(2, -9)

11)Which parent function to the following set of points belong?

{(-4, 5) (-2, 3) (0, 1) (2, -1) (4, -3) }A) y =

B) y =

C) y = x

D) y =

Plot the points !!!

What is the equation of the line through the points? y = -x + 1

12) Name the type of graph for eachCHOICES: LinearQuadraticExponentialInverse VariationDirect Variation

A B

C DE

Exponential Quadratic

Linear& Direct Variation

InverseVariation Linear