Quadratic Functions

Discriminants

100

What is the algebraic expression for the discriminant?

b^2-4ac

200

If the discriminant is greater than zero, are my roots real/imaginary AND are they equal/unequal?

real AND unequal

300

If the discriminant is less than zero, are my roots real/imaginary AND are they equal/unequal?

imaginary AND unequal

400

If the discriminant is equal to zero, are my roots real/imaginary AND are they equal/unequal?

real AND equal

500

James calculated the discriminant of a quadratic: 

(3)^2-4(2)(-2)

Are his roots real/imaginary AND are they equal/unequal?

real AND unequal

A Complex Life

100

i^23

-i

200

(6-i)-(22+3i)

-16-4i

300

(4-i)(3+2i)

12+8i-3i-2i^2

12+5i-2(-1)

14+5i

400

4x i(3i-i)^2

4x i(2i)^2

4x i(4i^2)

4x i(4(-1))

4x i(-4)

-16x i

500

(4-isqrt(2))(4+isqrt(2))

16+4isqrt(2)-4isqrt(2)-i^2(sqrt(2))^2

16-(-1)(2)

16+2

18

Gettin' Radical

100

sqrt(72)

sqrt(72)

sqrt(36)*sqrt(2)

6sqrt(2)

200

sqrt(112)

sqrt(112)

sqrt(16)*sqrt(7)

4sqrt(7)

300

sqrt(-49)-sqrt(-25)

sqrt(-49)-sqrt(-25)

7i - 5i

2i

400

sqrt(-44)

sqrt(-44)

sqrt(-1)*sqrt(4)*sqrt(11)

2isqrt(11)

500

2sqrt(-175)

2sqrt(-175)

2*sqrt(-1)*sqrt(25)*sqrt(7)

2i*5sqrt(7)

10isqrt(7)

Solvin' Quadratics

100

Matt is solving by factoring. What is his next step?

x^2-2x=8

x^2-2x-8=0

(    )(    )=0

(x-4)(x+2)=0

200

Solve:

x^2+17=0

x^2+17=0

x^2=-17

sqrt(x^2)=pmsqrt(-17)

x=pmisqrt(17)

300

Solve:

x^2-12x+3=-33

x^2-12x=-36

x^2-12x+(-6)^2=-36+(-6)^2

x^2-12x+36=-36+36

(x-6)(x-6)=0

x=6

400

Solve: 

x^2+16x-61=0

x^2+16x-61=0

x^2+16x=61

x^2+16x+(8)^2=61+(8)^2

x^2+16x+64=125

(x+8)^2=125

sqrt((x+8)^2)=pmsqrt(125)

x+8=pm5sqrt(5)

x=-8pm5sqrt(5)

500

Solve:

x^2+8x+20=0

x^2+8x+20=0

x^2+8x=-20

x^2+8x+(4)^2=-20+(4)^2

x^2+8x+16=-20+16

(x+4)^2=-4

sqrt((x+4)^2)=pmsqrt(-4)

x+4=pm2i

x=-4pm2i

More Solvin' Quadratics

100

Julia is solving by factoring. What is her next step?

x^2=2x+35

? = 0

x^2=2x+35

x^2-2x-35=0

200

Solve:

x^2-10=12

x^2-10=12

x^2=22

sqrt(x^2)=pmsqrt(22)

x=pmsqrt22

300

Solve:

16x-61=-x^2+3

16x-61=-x^2+3

x^2+16x-64=0

x^2+16x+(8)^2=64+(8)^2

x^2+16x+64=64+64

(x+8)(x+8)=128

(x+8)^2=128

sqrt((x+8)^2)=pmsqrt(128)

x+8=pm8sqrt(2)

x=-8pm8sqrt(2)

400

Solve:

x^2-20x+101=0

x^2-20x+101=0

x^2-20x=-101

x^2-20x+(-10)^2=-101+(-10)^2

x^2-20x+100=-101+100

(x-10)(x-10)=-1

(x-10)^2=-1

sqrt((x-10)^2)=pmsqrt(-1)

x-10=pmi

x=10pmi

500

Solve:

x ^2 +10x+50=0 

x^2 +10x+50=0

x^2+10X=-50

x^2+10x+(5)^2=-50+(5)^2

x^2+10x+25=-50+25

(x+5)^2=-25

sqrt((x+5)^2)=pmsqrt(-25)

x+5=pm5i

x=-5pm5i