Solving Linear Systems
Solve the linear system: x+y=15, 9x-y=15
x=3, y=12
What are the roots of the the quadratic: x2+10x+21=0
Turn -x+y=-15 into slope-intercept form.
y=x-15
Find the product of the monomials: 4x4y and x2y
4x6y2
(2x2+5)+(x2+12)
3x2+17
Solve the linear system: x-y=-15, x+5y=9
y=4, x=-11
Find the roots of the parabola described by the quadratic: 2x2-x=10
x=5/2, x=-2
Turn 2y+3x=12 into slope intercept form.
y=-3/2x+6
Find the product of the monomials: -15x2y13 and 6x7y3
-90x9y16
(x2+2x-1)+(5x2+12x-12)
6x2+14x-13
Find the solution to the system: x+y=17, 5x+12y=120
x=12, y=5
Find the roots of the parabola y=12x2+30x
x=0, x=5/2
Turn 10x-12y=24 into slope-intercept form.
y=5/6x-2
Multiply the binomials: (3x+2)(2x-12)
6x2-32x-24
(3x-13)-(6x+1)
-3x-14
Solve the linear system: y=3x+12, y=5x+2
x=5, y=27
Find the roots and the vertex of the following parabolic function: y=x2+4x-12
Is is concave up or concave down?
x=-6, x=2
vertex: (-2, -16)
Concave up
What is the slope of a line parallel to 8x-16y=30?
m=1/2
Multiply the binomials: (3x2+10)(4x+5)
12x3+15x2+40x+50
(-x2+12x-1)-(5x2+5x-4)
-6x2+7x+3
Solve the linear system: 2y+3x=7, 6x+4y=14
Infinite Solutions
Find the roots and the vertex of the parabolic function: f(x)=-2x2+4x
Is it concave up or concave down?
Roots: x=0, x=2
Vertex: (1, 2)
Concave down
What is the slope of a line perpendicular to 2y+4x=16?
(hint: the slopes of perpendicular lines are "opposite-reciprocals" to each other)
m=-1/2
Multiply the polynomials: (x2+3x+1)(5x-3)
5x3+12x2-4x-3
(2x2-3x+20)+(-x3+4x-12)
-x3+2x2+x+8