Inequalities
x<6
Find the solution to the system of equations:
x+y=-5
x-y=5
(0,-5)
Simplify: (2a-3b)+(-4a+5b)
-2a+2b
Factor: 10x+45y
5(2x+9y)
Does the function have maximum or minimum:
y=-4x2-5x+25
maximum
Solve the inequality:
-3x>18
x<-6
Find the solution to the system of equations:
x+2y=-5
4x+8y=-20
Infinitely many solutions
Simplify:
3x(x2-4x+5)
3x3-12x2+15x
Factor: a2-5ab+3a-15b
(a+3)(a-5b)
What is the graph of a quadratic function called?
Parabola
When graphing inequalities what does an open circle mean versus a closed circle?
Open circle: < or >
Closed circle: < or equal to or > or equal to
Describe what the graph of a system of equations looks like when there are...
infinite solutions
no solution
one solution
infinite solutions-same line
no solution-parallel lines (no intersection)
one solution-one point of intersection
Simplify: (x+2)(x-2)
x2-4
(x+2)(x+5)
Write the equation of the quadratic function that passes through: (0,3) and (5,-22)
y=-1x2+3
Solve the inequality and graph the solution on a number line:
2x>6 or x-3<-2
x>3 or x<1
Check graph
Write a system of equations for the scenario:
A theater sold 102 tickets for a play. Adult tickets cost $21 and student tickets cost $15. Total ticket sales were $1,932. Let x represent the number of adult tickets sold and y represent the number of student tickets sold.
x+y=102
21x+15y=1932
Simplify:
(2x+5)(x-3)
x2-x-15
Factor: x2-121
(x+11)(x-11)
Graph the equation and identify the axis of symmetry, vertex, x-intercepts, and y-intercepts
y=x2-2x-15
Axis of symmetry: x=1
Vertex: (1,-16)
x-ints: -3 and 5
y-int: -15
Solve the compound inequality and graph the solution on a number line.
3<3x+3<12
0<x<3
Check graph
Is (6, -6) a solution to the system of inequalities? How do you know?
y<x-6
y>-2x+2
Yes (in the overlap)
Simplify:
(x-8)2
x2-16x+64
Factor: 2x2-5x+3
(2x-3)(x-1)
Solve the equation: x2-5x+8=0
No real solution