Quadratics
Graph the quadratic and identify the vertex:
y=(x-4)^2-4
Desmos Graph
Use the leading coefficient test to describe the left hand and right hand behavior of the graph:
f(x)=x^3+2x
x->-oo, f(x)->-oo; x->oo, f(x)->oo
Find zeros of the polynomial:
f(x)=x^3-12x^2+36x
x=0, x=6
Perform the given operation:
[(x^2-x-2)/(x^2-16)-:(x^2-4x-5)/(3x+12)]*(x^2-9x+20)/(5x-10)
3/5
Perform the given operation:
2i-(6+5i)+(2-3i)
-4-6i
Identify the V.A. and H.A:
(2x+1)/(x-2)
V.A., x=2; H.A., y=2
Graph the quadratic and identify the vertex:
y=-2x^2+8x+1
Desmos Graph
Use the leading coefficient test to describe the left hand and right hand behavior of the graph:
f(x)=-2x^5+5x^3-1
x->-oo, f(x)->oo; x->oo, f(x)->-oo
Find the zeros of the polynomial:
f(x)=4x^4-20x^3+16x^2
x=0, x=1, x=4
Perform the given operation:
(5x+4)/(x^2-4)+3/(x-2)
((5x+4)+3(x+2))/((x-2)(x+2)
Perform the given operation:
(4-6i)+(9-11i)-(4-7i)
9-10i
Identify the V.A. and H.A:
(x+2)/(x^2-4)
V.A., x=2,-2; H.A., y=0
Find the x-intercepts of
f(x)=2x^2+11x-13
x=-13,2
Write the equation of the polynomial that has zeros:
x=-2, x=3, x=3/4
y=4x^3-7x^2-21x+18
Use the rational root theorem to find all the rational zeros:
f(x)=8x^4-14x^3-71x^2-10x+24
x=-2, x=-3/4, x=1/2, x=4
Perform the given operation:
(x-2)/(3x^2-9x)-(x+1)/(2x^2)
(2x(x-2)-3(x+1)(x-3))/(6x^2(x-3)
Perform the given operation:
(2-4i)(6-9i)
-24-42i
Identify the V.A. and H.A:
(x+6)/(x^2-3x-4)
V.A., x=4,-1; H.A., y=0
Write the equation of the function that has a vertex of (2,-4) and passes through the point (5,-6)
y=-2/9(x-2)-4
Write the equation of the polynomial that has zeros:
x=-2, x=5i
x^3+2x^2+25x+50
Find all the zeros given x=3i is a zero of the polynomial:
x^4+3x^3-x^2+27x-90
x=3i, -3i, 2, -5
Solve the rational equation:
(2x^2+5x-2)/(x+4)=x
x=-2,1
Perform the given operation:
(3+i)/(5-2i)
(13+11i)/29