Algebra 2 Semester Test Review
write an equation in slope-intercept form for the line that satisfies the conditions slope=-2 and passes through (-3,-5)
y=-2x-11
Which quadratic function has its vertex at (-2,7) and opens down?
y=-3(x+2)^2+7
write an equation in slope-intercept form for the line that satisfies the conditions passes through (-2,4) and (0,8)
y=2x+8
write an equation for the line that passes through (1,2) and is parallel to y=4x-3
y=4x-2
passes through (3,5) and (-1,5)
y=5
Is the relation a function? {(-3,0),(0,2),(2,4),(4,5),(5,2)}
yes
Is the relation a function? {(1,2),(3,4),(5,6),(7,8)}
yes
is the function linear? 3x+4y=12
yes
is the function linear? f(x)=-2x+9
yes
is the function linear? y=6x-19
yes
scatter plot
A graph with points plotted to show a possible relationship between two sets of data.
for the system of inequalities y>0, x>0, and y<-2x+4 find the minimum value of f(x,y)=3x+y for the feasible region
0
write the equation in standard form and id A,B, and C y=12x
12x-y=0 A=12 B=-1 C=0
square matrix
a matrix with the same number of rows and columns
cramer's rule
a method that uses determinants to solve a system of linear equations
dependent
a system of equations that has an infinite number of solutions
unbounded
a system of inequalities that forms a region that is open
Name the sets of numbers to which -1/3 belongs.
rational, reals
substitution method
the first step in solving a system of equations is to solve on equation for one variable in terms of the others
inverse
the n x m matrix whose product is an identity matrix when multiplied by another n x m matrix
for the system of inequalities y>0, x>0, and y<-2x+4 find the coordinates of the vertices of the feasible region
(0,0),(2,0),(4,0)
simplify (4-2i)/(7+3i)
(11-13i)/29
find the number and type of roots for x^2 +10 = 12x - 16
1 real, rational
Evaluate matrix A on the board using diagonals
10
One number is four times a second number. If you take oe-half of the second number and increase it by the first number, the result is at least 45. Find the least possible value for the second number.
10
Simplify (1/3)(15x-9)+(1/5)(25x+5).
10x-2
f(x)=-3x+2 find f(0)
2
find the number and type of roots for 2x^2 -7x +9=0
2 complex
Which quadratic equaiton has roots -2 and (1/5)?
5x^2+9x-2=0
for the system of inequalities y>0, x>0, and y<-2x+4 find the maximum value of f(x,y)=3x+y for the feasible region
6
Find the value of c that makes x^2 - 9x + c a perfect square.
81/4
5(2x-6)=7x-3
9
Jamie is 4 years younger than her brother. Five years from now, the sum of thier ages will be 32. Find Jamie's present age.
9
inconsistent
A system of equations that has no solution.
For the matrices written on the board find the inverse of matrix Q
P
5x-4≥26 or 29-3x>2
all real numbers
At a university, 1200 students are enrolled in engineering. There are twice as many in electrical engineering as in mechanical engineering, and three times as many in chemical engineering as there are in mechanical engineering. Write a system of equations that represents the number of students in each program
c+m+e=1200, 2m=e, 3m=c
Determine whether f(x)=4x^2-16x+6 has a maximum or a minimum value and find that value.
minimum; -10
scalar multiplication
multiplying any matrix by a constant called a scalar; the product of a scalar k and an m x n matrix
Is the relation a function? {(-4,1),(3,3),(1,1),(-2,5),(3,-4)}
no
is the function linear (1/x)+3y=-5
no
feasible region
the intersection of the graphs in a system of constraints
write the equaion in standard form and id A,B, and C 4x=8y-12
x-2y=-3 A=1 B=-2 C=-3
The quadratic equation x^2 -8x=-20 is to be solved by completing the square. Which equation would be a step in that solution?
x-4=±2i
0.38>(2x-7/5)
x<4.45
Solve x^2≥2x+24
x≤-4 or x≥6
point slope form
y-y₁=m(x-x₁)
Write an equation for the parabola whose vertex is at (-8,4) and passes through (-6,2)
y=(-3/2)(x+8)^2 +4
for the system of inequalities: x>2, y-x>-3, and x+y<5 find the coordinates of the vertices of the feasible region.
(2,-1),(2,3),(4,1)
To solve 9x^2-12x+4=49 by using the square root property, you would first rewrite the equation as
(3x-2)^2=49
Find the exact solutions to 3x^2=5x-1 by using the Quadratic Formula
(5±√13)/6
Identify the vertex, axis of symmetry, and direction of opening for y=(1/2)(x-8)^2 +2
(8,2); x=8; up
Simplify (4-12i)-(-8+4i)
12-16i
What is the value of y in the solution fo the system of equations? 2x+y+z=1 2x-y-3z=-3 x-2y-4z=-2
-8
f(x)=-3x+2 find f(-3)
11
23=5-(2/3)m
-27
|2x-3|≤7
-2≤x≤5
Evaluate 2b(4a-c^2) if a = 5, b = 3/2, and c = 11
-303
f(x)=-3x+2 find f(y)
-3y+2
For the matrices written on the board find the determinant of P
-4
Solve -x^2=4x by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.
-4, 0
f(x)=-3x+2 find f(2w)
-6w+2
Evaluate -|3c-d| if c=-1 and d=5
-8
find the slope that passes through the pair of points (8,2) and (2,8)
-1
f(x)=-3x+2 find f(4)
-10
for the system of inequalities: x>2, y-x>-3, and x+y<5 find the minimum value of f(x,y)=x-4y for the feasible region
-10
find the slope that passes through the pair of points (2,5) and (6,-3)
-2
the first equation of the system is multiplied by 3. By what number would you multiply the second equation to eliminate the x variable by adding? 4x-3y=6 6x+1y=10
-2
Write a quadratic equation with roots ±(i√3)/4
16x^2+3=0
One side of a triangle is four centimeters longer than the shortest side. The third side of the triangle is twice as long as the shorest side. Find the length of the longest side of the triangle if its perimeter is 40 centimeters.
18
Select the algebraic expression that represents the verbal expression twice the sum of a number and 8.
2(n+8)
At a university, 1200 students are enrolled in engineering. There are twice as many in electrical engineering as in mechanical engineering, and three times as many in chemical engineering as there are in mechanical engineering. how many students are enrolled in the mechanical engineering program?
200
The formula for the surface area of a sphere is A = 4pir^2, where r is the length of the radius. Find the surface area of a sphere with a radius of 14 feet. Use (22/7) for pi.
2464 ft^2
write the equation in standard form and id A,B, and C -4y=3x-24
3x+4y=24 A=3 B=4 C=24
Find the value of |₃⁵ ₂¹|
7
Identify the y-intercept and the axis of symmetry for the graph of f(x)=10x^2+40x+42
42; x= -2
for the system of inequalities: x>2, y-x>-3, and x+y<5 find the maximum value of f(x,y)=x-4y
6
the first equation of the system is multiplied by 2. By what number would you multiply the second equation to eliminate the y variable by adding? 4x-3y=6 6x+1y=10
6
write the equation in standard form and id A,B, and C 2x+5y=10
A=2 B=5 C=10
the 300 students at Holmes School work a total of 5000 hours each month.Each student in group A works 10 hours, each student in group B works 15 hours, and each in group C works 20 hours each month. There are twice as many students in group B as in Group A. Write the equations for the system.
A=2B A+B+C=300 10A+15B+20C=5000
State the domain and range of the relation {(-3,0),(0,2),(2,4),(4,5),(5,2)}
D:{-3,0,2,4,5} R:{0,2,4,2}
State the domain and range of the relation {(-4,1),(3,3),(1,1),(-2,5),(3,-4)}
D:{-4,3,1,-2} R:{1,3,5,-4}
State the domain and range of the relation {(1,2),(3,4),(5,6),(7,8)}
D:{1,3,5,7} R:{2,4,6,8}
domain
The set of all first coordinates (or x-values) of a relation or function.
one-to-one function
a function where each element of the range is paired with exactly one element of the domain
For the matrices written on the board find the first row of RS
[0 14]
Name the property illustrated by 5(x+y)=5(y+x).
commutative property of addition
describe the system of equations: 9x-3y=15 and 6x=2y+10
consistent and dependent
describe the system of equations 3x+y=3 x-2y=4
consistent and independent
how many solutions does the system of equations: y=-3x-7 and y=3x-7 have?
exactly one solution
A system of linear equations may not have
exactly two solutions
constraints
in linear programming, the name of the inequalities
describe the system of equations: 2x-y=4 and 4x-2y=6
inconsistant
describe the system of equations 4x-2y=-6 2x-y=8
inconsistent
would you shade the left or right side of the line for x-3y<6
left
would you shade the left or right side of the line for y>2x+1
left
identity function
linear equation y = x, graph is a line going through origin and 1st and 3rd quadrants at 45 degree angles
2|m+7|>8
m<-11 or m>-3
is the function linear? x²+y²=4
no
is the function linear? y=x³-6
no
For the matrices written on the board find the first row of 4P-S
not possible
elimination method
one step in the process is to add the equations
linear programming
the process of finding the maximum or minimum values of a function for a region defined by inequalities
write an equation in slope-intercept form for the line that satisfies the conditions slope=(2/3) and passes through (4,-1)
y=(2/3)x-(11/3)
write an equation for the line that passes through (-3,5) and is perpendicular to y=(2/3)x-8
y=(-3/2)x+(1/2)
Write y=x^2 +4x - 1 in vertex form.
y=(x+2)^2 - 5
Solve x^2-3x=18 by factoring
{-3,6}
18=3|4x-10|
{1,4}
Carlos expects the grade on his next Algebra test to be between 75 and 85. Using g to represent Carlos's test grade. write an absolute value inequality to describe this situation.
|g-80|<5
9≤7-x≤-1
∅
|x-3|+10=2
∅