review for eoc algebra. 1) in the quadratic equation x² – x + c = 0, c represents an unknown...
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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