Key features
Find the Key features of y=5/2(x+5)(x+1)(x-2)
x-ints: (-5,0),(-1,0),(2,0)
y-int:(0,-25)
Vertical Stretch b/c the "a" is bigger than 1.
degree: 3 b/c there are 3 points with three invisible ones and they are all added together.
end behavior: Down and up b/c it has an odd degree and a positive "a".
Write and polynomial equation for a graph that goes through the point (-1,6) and has x-intercepts at (-2,0), (1,0), and (3,0).
y=3/4(x+2)(x-1)(x-3)
Sketch and describe a graph with x-intercepts at -1,4, and 5, that has end behavior of down and up.
The graph starts in the bottom left, goes up across the x-axis at -1, turns and crosses at 4, then turns again and crosses at 5 before extending up and to the right.
What are the two roots of this equation: x3+3x2-7x-21
x=2.64
x=-2.64
How many real roots are there? How many complex roots?
The graph starts in the top left, goes down and crosses the x-axis, then turns up, and turns again before hitting the axis. It then turns one last time and crosses the x-axis again.
2 real roots
2 complex roots
Find the key features of the equation: y=1/28(x+3)(x-2)2(x-5)
x-inter:(-3,0),(2,0),(5,0)
y-inter:(0,-2.14)
Vertical Shrink b/c the "a" is smaller than 1.
Degree: 4 b/c there is 2 invisible ones and an exponent of 2, so they are all added together.
End Behavior: Up and Up b/c the degree is even and the "a" is positive
Write and polynomial equation for a graph that bounce off the x-axis at (-1,0), crosses it at (3,0), and goes through the point (1,-4).
1/2(x+1)^2(x-3)
Sketch and describe a graph with x-intercepts at -10,-7, and 12, that has end behavior of down and up.
The graph starts in the bottom left, goes up across the x-axis at -10, turns and crosses at -7, then turns again and crosses at 12 before extending up and to the right.
What are the two roots for this equation: x3-2x2-5x+10
x=5
x=-1
How many real roots? How many complex roots?
The graph starts in the top left, goes down and crosses the x-axis, then turns up, and turns again before hitting the axis. It then turns one last time and crosses the x-axis again.
2 real roots
2 complex roots
Find the key features of the equation: y=1/2(x+1)2(x-2)
x-inter: (-1,0),(2,0)
y-inter: (0,-1)
Vertical shrink b/c the "a" is smaller than 1.
Degree: 3 b/c there is an exponent of 2 and an invisible 1 that are being added together.
End Behavior: Down and Up b/c the odd degree and the positive "a".
Write and polynomial equation for a graph that bounce off the x-axis at (2,0), crosses it at (5,0) and (-3,0), and goes through the point (4,-1).
y=1/28(x+3)(x-5)(x-2)^2
Sketch and describe a graph represented by the equation y=x(x+5)(x-3)2
The graph starts in the top left, goes up across the x-axis at -5, turns and crosses at 0, then turns again and bounces off of the x-axis at 3 before extending up and to the right.
What are the two roots for this equation: x3+x2-7x-7
x=2.37
x=-3.37
Factor x3+3x2+x-5 if one factor is (x-1).
There are 2 complex roots.
(x-1)(x-(-2+i))(x-(-2-i))