Math 2 U5L2 Review

Standard Form--> Vertex Form

100

x^2+4x+4

(x+2)^2

200

x^2+4x+5

(x+2)^2+1

300

x^2+16x-7

(x+8)^2-71

400

x^2-14x-3

(x-7)^2-52

500

x^2-5x+12

(x-2.5)^2+5.75

(x-5/2)^2+23/4

Vertex Form--> Standard Form

100

(x+3)^2

x^2+6x+9

200

(x+6)^2-4

x^2+12x+32

300

(x-5)^2+7

x^2-10x+32

400

(x-11)^2-8

x^2-22x+113

500

3(x+2)^2+9

3x^2+12x+21

Solving Quadratics

100

Solve

0=x^2+4x-5

x=-5

or

x=1

200

Solve

0=(x+4)^2-25

x=1

or 

x=-9

300

Solve

0=(x-7)^2+81

x=7+-9i

400

Solve

0=x^2-12x+27

x=6+-3i

500

Solve

-212=3(x+5)^2+220

x=-5+-12i

Number of Solutions

100

How many real solutions does f(x)=x^2-8x+3 have?

2 real solutions

(-8)^2-4(1)(3)

64-12

52>0

200

How many real solutions does h(x)=2x^2-7x+10 have?

0 real solutions

(-7)^2-4(2)(10)

49-80

-31<0

300

g(x)=2x^2-10x+c

Find a value for c  that allows  g(x) to have 2 real solutions.

Any number that is less than 12.5

c<12.5

400

g(x)=2x^2-10x+c

Find a value for c  that allows  g(x) to have 1 real solutions.

c=12.5

500

g(x)=2x^2-10x+c

Find a value for c  that allows  g(x) to have 0 real solutions.

Any number that greater than 12.5

c>12.5

Equation Based on the Vertex

100

Minimum at (1,5)

f(x)=(x-1)^2+5

200

Minimum at (4,-7)

f(x)=(x-4)^2-7

300

Maximum at (-6,10)

f(x)=-(x+6)^2+10

400

Minimum at (-13,-2)

f(x)=(x+13)^2-2

500

Maximum at  (-1/2,4) 

f(x)=-(x+1/2)^2+4