Polynomials
Simplify (2x+5)2
4x2+20x+25
Hint: expand and foil or use identity (a+b)2=a2+2ab+b2
What is the vertex of:
y = (x-3)2+4
(3, 4)
Simplify
sqrt(25x^4y^3
What is
5x^2ysqrty
Evaluate log39
What is 2?
hint: think the base to what power is the argument (or do change of base)
Simplify (2+5i)(4-3i)
23+14i
hint: foil, change i2 to -1
f(x) = 2x4-3x3+2 g(x) = x3+2x2-5
Find f(x) - g(x)
2x4-4x3-2x2+7
hint: distribute the negative to g(x) when subtracting
Describe the transformation of:
y = 3(x+2)2+4
stretch by 3, shift left 2, up 4
hint: a = 3, h = -2, k = 4
(-64)2/3
What is 16?
hint:
(root(3)(-64))^2
Is y = 3(1/4)x growth or decay?
Since b = 1/4 and < 1
decay
What are the zeros and end behavior of
f(x) = 2x(x+3)(2x-1)
x = 0, -3, 1/2
End Behavior: down/up
(odd degree (3), pos LC)
What is the end behavior of
3x4-2x3+7x2-5x
up/up
hint: degree is 4 (even), LC is 3 (pos)
Write vertex form quadratic equation if:
shifted right 2, up 3
y = (x-2)2+3
hint: y = a(x-h)2+k
Simplify
(2+sqrt3)(2-sqrt3)
What is 1?
hint:
4-(sqrt3)^2
Amount if $1200 dposited at 2.5% compounded continuously for 5 years
What is $1359.78
hint: 1200e(.025)(5)
Solve by factoring
3x3 + 6x2- 24x
x = 0, -4, 2
hint: pull out gcf of 3x, then factor
Use remainder theorem to evaluate P(2) for
3x4-2x3+3x2+2x-1
p(2) = 47
hint: use synthetic division to get the remainder of 47.
Convert to standard form:
y = 2(x+1)2-3
y = 2x2+4x-1
hint: 2(x+1)(x+1)-3
41/342/3
What is 4?
hint: 43/3
Expand log3(2x2)
log3 2 + 2log3 x
Factor 4x2+25
(2x+5i)(2x-5i)
hint: sum of squares (like diff of squares with complex numbers)
Divide x3-4x2+2x-1 by (x-1)
x^2-3x-1-2/(x-1)
What is the vertex of
y = 2x2+4x+1?
(-1,-1)
hint: find x = -b/2a, plug in to get y.
Solve
sqrt(4x+2)-2=-4
x = 1/2
x = 10
Solve
4/a +5/(3a) =3
a = 17/9
hint: multiply all terms by LCD of 3a