Complete the square/Using the square root property
4x2 + 25 = 125
x= 5 or x = -5
m2 − 5m − 14 = 0
{7, −2}
Find all solutions to the polynomial:
y=x2+7x+12
x = -3, -4
Write a polynomial with the following roots:
x = 3, -4
Sketch a graph of the quadratic. Include the vertex.
y = (x-1)2+6
Vertex: (1,6)
34 = (a - 2)2 - 2
a = 8 or a = -4
7r2 + 84 = -49r
-4, -3
Find all solutions to the polynomial:
y=x3+3x2-16x-48
x = 4, -4, -3
Write a polynomial with the following roots:
x = -2, -4, 5, 7
Sketch a graph of the quadratic. Include the vertex and end behavior.
y = x2+5x+6
vertex: (-5/2, 1/4)
x-int: (-3,0) cross, (-2,0) cross
Even/Positive -> starts and ends positive
(4x + 1)2 - 16 = 0
x = 3/4 or x = -5/4
x2 − 10x + 26 = 8
{5 + square root 7, 5 square root − 7}
Find all solutions to the polynomial:
y=2x3+x2+8x+4
x = (-1/2), 2i, -2i
Write a polynomial with the following roots:
x = 2, 2i, -2i
y = x3-2x2-4x+8
Sketch a graph of the polynomial. Include all x-intercepts, y-intercepts, and end behavior.
y = x4-2x3+x2
y-int: (0,0)
x-int: (0,0) touch, (1,0) touch
Even/Positive -> starts and ends positive
Solve x2-2x=23 for x by completing the square
x=1+2squarerootof6
x=1-2squarerootof6
9n2 = 4 + 7n
{ 7 + square root of 193 / 18, 7 - square root of 193 / 18}
Find all solutions to the polynomial:
y=x4-20x2+64
x = 4, -4, 2, -2
Write a polynomial with the given roots:
x = 3 + 2i, 3, -4
y = x4-5x3-9x2+81x-108
Sketch a graph of the polynomial. Include all x-intercepts, y-intercepts, and end behavior.
y = 6x5+4x4-9x-36
y-int: (0,-36)
x-int: (-4,0) cross, (sqrt(3),0) cross, (-sqrt(3),0) cross
Odd/Positive -> start negative end positive
Solve x2-8x=68 for x by completing the square.
x=4+3squarerootsof14
x=4-3squarerootsof14
9n2 = 4 + 7n
Round to the nearest thousandth
x = -0.383 or x = 1.161
Find all solutions to the polynomial:
y=x8-17x4+16
x = 1, -1, i, -i, 2, -2, 2i, -2i
Write a polynomial with the given roots:
x = -1, -2i, -3, -4i
y = x6+4x5-17x4-80x3+4x2+256x+192
Sketch a graph of the polynomial. Include all y-intercepts, x-intercepts, and end behavior.
y=-x5
y-int: (0,0)
x-int: (0,0) cross
Odd/Negative -> start positive end negative