Complex Numbers

Find that vertex!

Operations with Complex Numbers

Parabola Party

solving complex numbers

100

Find the vertex of the parabola:

3y = (x+7)² + 12

(-7, 4)

100

(3i)(8i)=

-24

(3x8)=24 (ixi)=i²=-1

(24)(-1)

100

Identify the AOS, max or min. Graph it.

y = (x + 3)² - 5

AOS: x = -3

Min at -5

100

x² + 40 = 4

6i, -6i

200

Find the vertex of the parabola:

y - 6 = (x - 2)² + 1

(2, 7)

200

(2+4i)(3+5i)=

-14+22i

Foil: 6+10i+12i+20i²

Combine like terms: 6+22i+20i²

Simplify i²: 6+22i-20

Combine again:

200

Identify the AOS, max or min, x-intercepts, and y-intercept.

y = 4x² - 100

AOS: x = 0. Min at -100

(5, 0), (-5, 0), (0, -100)

200

x² + 41 = 10x

5 + 4i, 5 - 4i

300

Find the vertex of the parabola:

y = (x + 9)(x + 1)

Vertex (-5, -16)

300

(2-4i)(3-5i)=

-14-22i

Foil:6-10i-12i+20i²

Simplify: 6-22i-20

Combine like terms:

300

Identify the AOS, max or min, x-intercepts, and y-intercept.

y = x² + 2x - 63

x = -1, Min at -64

(7, 0), (-9, 0), (0, -63)

300

x² + 8x + 41 = 0

-4 + 5i, -4 - 5i

400

Find the vertex of the parabola:

y = (x + 10)(x - 2)

(-4, -36)

400

5i / (2-4i)

-1 + 1/2 i

400

Identify the AOS, max or min, x-intercepts, and y-intercept.

y = -2x² + 16x - 32

AOS: x = 4, max at 0

(4, 0) and (0, -32)

400

Show TWO ways to solve

x² - 6x + 45 = 0

3 + 6i, 3 - 6i

500

Find the vertex of the parabola:

y = x² + 12x + 100

vertex (-6, 64)

500

Multiply (-5 + 7i) by its conjugate

(-5 + 7i)(-5 - 7i) = 74

500

Write the equation of a parabola with x-intercepts 2 and -5 that goes through (1,-24). Use standard form.

y = 4(x - 2)(x + 5)

y = 4x² + 12x - 40

500

Show TWO ways to solve

x² + 130 = 9

11i, -11i