Mult/Div Exponents
+/-/x Polynomials
Solving Quadratics
Quadratic Functions
A Little Factoring
100
Simplify.
2y・3xy²・6 =
36x6y3
100
(x² + 3x + 4) + (2x² - x -5)
x² + 3x + 4 + 2x² - x -5
3x² + 2x - 1
100
Solve for n.
n² + 9n + 20= 0
(n + 4)(n + 5) = 0
n = -4 or n = -5
100
- vertex
- axis of symmetry
- roots/zeros
- y-intercept
100
Factor.
6g3-9g2+12g
3g(2g2-3g+4)
200
Simplify.
((9gh^7l^6)^2)/(6g^3h^9l^6)
(27h^5l^6)/(2g)
200
(3x² - 4x + 7) - (2x² + 3 - 9)
3x² - 4x + 7 - 2x² - 3 + 9
x² - 4x + 13
200
Solve for r.
r² + 16 - 8r = 0
r² - 8r + 16 = 0
(r - 4)(r - 4) = 0
r = 4
200
Graph this equation.
f(x) = 2x2 + 1
200
Factor.
4v2 - 36w2
(2v+6w)(2v-6w)
300
Simplify, keeping it in scientific notation.
(3.11x107)(8.2x10-4)
25.502x103
300
2(x + 3) - 4(x² - 4)
2x + 6 - 4x²+ 16
- 4x² + 2x + 22
300
3h² - 17h + 20
3h² - 12h -5h + 20
(3h² - 12h) + (-5h + 20)
3h(h - 4) + -5(h - 4)
(3h - 5)(h - 4)
300
How would this graph look compared to f(x)=x2?
f(x)=-3(x-5)2-4
narrow or wider?
horizontal shift: ________
vertical shift: ________
direction of opening: up or down?
narrow
hor: 5 right
vert: 4 down
dir of open: down
300
Factor.
36z5+20z7-12z4
4z3(9z2+5z4-3z)
400
Simplify.
(2w^(6/11))(3w^(3/11))
6w^(9/11)
400
(x + 3)(x² + 5)
x^3 + 3x^2 + 5x + 15
400
Factor.
7f² + 29f + 4
7f² + 29f + 4
7f² + 28f + 1f + 4
7f(f + 4) + 1(f + 4)
(f + 4)(7f + 1)
400
f(x) = (1/4)(x+2)^2+7
Describe how the graph changed compared to f(x)=x2.
narrow or wider?
horizontal shift: ________
vertical shift: ________
direction of opening: up or down?
wider
hor: left 2
vert: up 7
dir of opening: up
400
Factor.
y2+3y-28
(n+2)(n-9)
500
Emily’s parents put $1,500 in her bank account for college tuition. At an interest rate of 8.25% compounded semiannually, what will be the balance after 18 years?
A=P(1+(r/n))^(nt)
A = 1500(1+(0.0825/2))^((2)(18))
$6,427.94
500
-3x(x-6)(x+6)
(-3x2 + 18)(x + 6)
= -3x3 - 18x2 + 18x + 108
500
Factor.
9 + 10t + t²
t² + 10t + 9
(t + 1)(t + 9)
500
Use the quadratic formula to solve for x of this equation:
8x2+10x-7 = 0
x = 0.5 or -1.75
500
Factor.
16a2-16ab+4b2
4(a2-4ab+b2)
4(a-b)2
or
(4a-2b)2