R U Absolutely Sure?
The absolute value of a number can either be
_?_ or _?_ but never _?_.
positive or zero but never negative
y = x2 is called the _?_ function for quadratics.
All other quadratic functions are simply translations/transformations of y = x2
parent
Factor using the Slide and Divide Method:
3x2 + x - 2
(x + 1)(3x - 2)
a) All quadratic equations have _?_ solutions.
b) The graph of a quadratic function is
called a _?_
a) two
b) parabola
Given 5x3 - 7 - 2x4
a) Rewrite in standard form
b) Classify the polynomial
a) -2x4 + 5x3 - 7
b) quartic trinomial
Solve for x:
|x + 3| - 4 = 2
x = 3 or x = -9
Given y = (x - 5)2 + 3
a) State the vertex
b) Is the vertex a maximum or a minimum
c) State the range using interval notation
a) (5,3)
b) minimum
c) [3,infinity)
Factor using the Slide and Divide Method:
4x2 + 21x + 5
(x + 5)(4x + 1)
The graph of a parabola can do one of three possible things regarding the x-axis:
The parabola can cross the x-axis _?_,
touch the x-axis _?_, or _?_.
twice, once, not cross/touch
Given (3x + 1)(2x2 - x + 4)
a) Multiply and write in standard form
b) Classify the polynomial
a) 6x3 - x2 + 11x + 4
b) cubic polynomial
Solve:
-4|x + 2| > 8
No Solution
Given y = -2(x + 8)2 - 4
a) State the vertex
b) Is the vertex a maximum or a minimum
c) State the domain using interval notation
a) (-8,-4)
b) maximum
c) (-infinity, infinity)
Factor using the Slide and Divide Method:
9x2 - 6x + 1
(3x - 1)(3x - 1)
a) When a parabola touches the x-axis at one point this is called a _?_ root.
b) When a parabola doesn't touch/cross the
x-axis it has two _?_ roots.
a) double
b) imaginary
a) Using Synthetic Division divide
x4 - 10x2 - 2x + 4 by x + 3
b) Is x + 3 a factor of the dividend? Explain.
a) x3 - 3x2 - x + 1 + 1/(x+3)
b) No b/c there is a remainder
Given y = |x - 4| - 7
a) state the vertex
b) state two other ordered pairs on the graph
a) (4,-7)
b) (3,-6), (5,-6), (2,-5), (6,-5), etc.
Given y = x2 - 9
a) State the vertex
b) State the axis of symmetry
c) State the range using interval notation
a) (0,-9)
b) x = 0
c) [-9, infinity)
Find a quadratic equation with these zeros/roots:
x = -3 and x = 1/2
2x2 + 5x - 3 = 0
Use the Quadratic Formula to solve
y = 2x2 + 5x - 3
x = -3 and x = 1/2
Given y = -3x4 + 5x2 - 8
a) Is the right end rising/falling? Explain.
b) Is the left end rising/falling? Explain.
c) State the end-behavior for the graph:
As x approaches -infinity, y approaches _?_
As x approaches +infinity, y approaches _?_
a) falling b/c LC is negative
b) falling b/c degree is even
c) -infinity
-infinity
Given y = -5|x - 3| + 2
a) State the axis of symmetry
b) Does the graph have a maximum or minimum value at the vertex? Explain.
a) x = 3
b) maximum b/c the a value is negative
Given y = 2x2 - 8x + 5
a) State the vertex (Use x = -b/2a)
b) State the y-intercept as an ordered pair
c) State the range using interval notation
a) (2,-3)
b) (0,5)
c) [-3,infinity)
Find a quadratic equation with these zeros/roots:
x = 6 d.r.
x2 - 12x + 36 = 0
Use the Quadratic Formula to solve
y = x2 - 6
x = (6)1/2 (+ square root of 6)
x = -(6)1/2 (- square root of 6)
Given y = -6x2 - 4x + 5x3 + 9
a) Is the right end rising/falling? Explain.
b) Is the left end rising/falling? Explain.
c) State the end-behavior for the graph:
As x approaches -infinity, y approaches _?_
As x approaches +infinity, y approaches _?_
a) rising b/c LC is positive
b) falling b/c degree is odd
c) -infinity
+infinity