Quadratics Project

Standard/vertex form of quadratics

100

write in standard form

(x-1)² =1

x² -2x+2

200

whats the vertex?

g(x)=(x-1)²-9

(1,-9)

300

write in vertex form

2x²+5x+4=0

2(x+(5/4))²+(7/8)=f(x)

400

write in standard form 

2(x+(5/4))²+(7/8)=f(x) 

2x²+5x+4=0

500

Find the vertex

9x² +3x+18

(-6, 324)

forming quadratic equations

100

what is standard form of a quadratic equation?

f(x)=ax²+bx+c

200

what is vertex form?

f(x) = a(x – h)²+k

300

what is the quadratic formula?

-b±√(b²-4ac)/(2a)

400

write the equation of a parabola whose minimum is (-1,5) and the points (2,5) are on the parabola.

(2+1)² +5 =5

500

write the equation of a parabola whose minimum is (-100,500) and the points (200,500) are on the parabola.

(200+100)²+500=500

factoring quadratics

100

is this factored form or standard form?

(x-8)(x+1)=0

factored form

200

solve by factoring 

x²-x-6=0

(-2,3)

300

what number would complete the square

x²+5x+___

25/4

400

solve by factoring

12x²-59x+72=0

x=9/4

x=8/3

500

factor the equation:

4x²+12xy+9y²-9r²-24rs-16s²=0

(2x+3y+3r+4s)(2x+3y-3r-4s)

solving quadratic equations

100

how many solutions are there?

-2x²+3x-5=f(x)

2

200

solve:

6x²-5x+1=0

x=1/3

x=1/2

300

solve:

9x²-12x+4=0

x=2/3

400

solve:

x² +x-6

x=-3

x=2

500

solve:

4x²+2x-2

x=-1

x=0.5

Complex #'s, discriminant, applications of quadratic equations

100

what is i²

-1

200

what is i^{13495793481703782568713465783460856314085440}

√-1

300

find the discriminant 

4x³=-6x²-3x

-12

400

find the discriminant:

80x²-400x+10=0

156800

500

Lauren is standing on the top of the school. There is a fun trampoline on the ground, which is 6.3923 feet off the ground. The school is 293.293 feet tall. Lauren falls backwards without jumping and lands on the trampoline. How long will it take for Lauren to hit the trampoline. 

4.238 seconds