Find the vertex
Find the x-value of the vertex of y=x2+8x+8
x=-4
If an equation has a negative right after the equal sign, what transformation would you see on the graph?
A reflection.
The x-intercepts are -1 and 8.
What is the square root of negative 1?
i
Pythagorean Theorem
Find the vertex of y=2(x+2)2-5.
(-2,-5)
What transformations would be seen on the graph of y=(x+5)^2-9. Include numbers in your answer.
Left 5, Down 9
Solve x^2-81=0
x=+-9
What is (7-3i)+(-5+9i)
2+6i
How many hundreds of years ago did people start using complex numbers?
Find the vertex of y=-4x2-24x-20.
(-3,16)
What transformations would you see on the graph of y=3(x-7)^2+15? Include numbers in your answer.
Stretch 3, Right 7, Up 15
Solve x^2+80=0. Answers must be fully simplified.
x=+-4i sqrt 5
What is (-5+3i)-(4+7i)?
-9-4i
CDLXXVI
476
If Jack sells jars of salsa he might make money. His profit can be modeled by P=-5x^2+46x+19. What is the price he should sell at to make the most money possible?
$4.60
Write an equation that has been shifted down 6, reflected, and moved to the right 9.
y=-(x-9)^2-6
Solve y=0.5x^2-10x-5
x=10+-3sqrt10
What is i to the 79th power?
-i
Which historical empire was the first to use negative numbers?
The Chinese
If a rocket is launched into the air from a tower. Its height (measured in feet) is modeled by h=-16t^2+190t+55. How high up does the rocket go before it begins to fall?
619.06 feet
What is the name of the form we use for these equations? Its formula is y=a(x-h)^2+k
Vertex form
(2x-1)(x-5). x=1/2, x=5
Multiply (6-2i)(4+8i)
40+40i
Which famous mathematician (and philosopher) started using the x-y system to graph equations into shapes?
Rene Descartes