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Describe the end behavior of
f(x) = -2x3+17+11x8+15x2
As x goes to + infinity, f(x) goes to + infinity.
As x goes to - infinity, f(x) goes to + infinity.
Identify the vertex and max/min value and axis of symmetry
f (x) = x2 -18x+86
vertex:(9, 5) min value: 5
axis of symmetry: x=9
Find the value of c that completes the square. x2 + 6x + c
c=9
Solve for x:
4(x-1)2+2=10
1 + sqrt 2, 1 - sqrt 2
simplify: −2(−6x − 9) − 4(x + 9)
8x-18
Write the general equation of a quadratic in standard form, vertex form, and intercept form
standard: y=ax2+bx+c
vertex: y=a(x-h)2+k
intercept: y=a(x-p)(x-q)
Factor: x2 − 7x − 18
(x − 9)(x + 2)
Find the value of c that completes the square x2 + (7/13)x + c
49/676
Simplfy: (7+5i)(8-6i)
86-2i
Solve the system of linear equations:
2x-y-z=15
4x+5y+2z=10
-x-4y+3z=-20
(5, 0, -5)
Describe the transformation of the parent function represented by g.
g(x)=(x+10)2-3
The graph of g translates y=x2 10 units to the left and 3 units down
Factor: 3b3 -5b2 +2b
b(3b − 2)(b − 1)
Solve each function by completing the square x2 − 12x + 11 = 0
{11,1}
simplify
(p + 4)/(p2 +6p +8)
1/(p+2)
Solve the nonlinear system of equations:
3x2+y=-30x-76
y-44=2x2+20x
(-4, -4) and (-6, -4)
f (x) = -3x4+2x3+3x2 -12x-6; Find f (−2)
-46
Write an equation in intercept form for the parabola that has x-intercepts of 12 and -6 and passes through (14, 4)
y=(1/10)(x-12)(x+6)
Solve the equation by completing the square x2 + 14x − 15 = 0
{1,-15}
(n+3)/(n+2) ÷ ((n-1)(n+3))/((n-1)2)
(n-1)/(n+2)
Factor each and find all zeros. One zero has been given. f (x) = 5x3 + 4x2 -20x -16; 2
Factors to: f (x) = (5x + 4)(x + 2)(x − 2) Zeros: {-(4/5), -2, 2}
Use Pascal's triangle to simplify:
(2x-3)4
16x4-96x3+216x2-216x+81
Find the discriminant of each quadratic equation then state the number of real and imaginary solutions.
9n2 − 3n − 8 = −10
−63; two imaginary solutions
Solve by completing the square 6x2 − 48 = −12x
{2, −4}
Divide:
(7x3+x2+x) / (x2+1)
7x+1+ (-6x-1)/(x2+1)