Unit 2: Quadratic
What is the vertex?
y=3(x-2)2+1
(2,1)
Identify where the zeros are touching or crossing the x-axis.
f(x)=(x+2)(x-4)3(x+1)2
(-2,0) and (-1,0) are crossing
(4,0) is touching
Write the following using radical notation. Assume that all variables are positive real numbers.
4x2/5
4 then 5 on foot x under with 2 as exponent
Switch the form
5x=125
log5125=x
What could be an extraneous solution for this equation:
y=5/x-6
x=6
How does the graph of y = (x+4)2 compare with the graph of the parent function y = x2
translated 4 units to the left
Solve:
x4-5x2+4=0
x=-1,1,-2,2
Simplify the cube root of 54
3 cube root of 2
Evaluate lne8=x
x=8
What is the product
x(x-3) X (x-1)(x+3)
(x-1) x(x-3)
x+3
Simplify the expression
(4+i)(5+i)
19+9i
Factor completely.
5x3-2x2+15x-6
(5x-2)(x2+3)
Simplify
(3x3y)(4xy-5)
(5x2)3
12/(125x2y4)
What is the inverse of y=ln(x-1)
y-1=ex+1
What is the simplified form of
x2-10x-11/x2-1
x-11/x-1
Factor completely
9x2-81
9(x-3)(x+3)
What is the result when (3x3-4x2+6x-1) / (x-5)
3x2+11x+61+304/(x-5)
Solve.
square root(7x-3)=4
x=19/7
Solve 53x-1=1252x+5
x=-16/3
-4 - 3 = 1
x 5 5x
x=-21
Solve: x2+7x-1=0
-7+or - square root of 53 over 2
Sketch the graph of the polynomial.
f(x)= -(x-3)(x+5)(x+1)
Sketch
x-intercepts: 3,-5,-1
All crossing
y-intercept: 15
End Behavior: up/down
Simplify
5th root(7x10y11)
x2y2 5th root(7y)
Solve log3(2x-1)=2
x=5
Sketch the graph
f(x)=5/(x-1)
Sketch
x=1
y=0
(0,-5)