Factorization
Graphs
Forms of Quadratics
Word Problems
100
Factor 3x2-5x-2.
(3x-1)(x+2)
100
Write the equation for this graph in factored form.
3/2(x-4)(x+7)
100
Write 2x2+5x-12 in factored form.
(2x-3)(x+4)
100
Justin is skiing down a slope when he launches himself into the air, does a flip, and lands further down the cliff. Suppose his height in meters is described by the equation h(t) = -2t2+9t+10. After how many seconds does he get to the highest height he reaches?
4.5 seconds
200
Complete the factorization:
8z3+38z2+57z+77 = (2z+7) ( .... ? ....)
4z2+5z+11
200
Write the equation for this graph in vertex form:
-1/5(x-4)^2+17/8
200
Write
6(x+5/3)^2-2
in standard form.
6x2+20x+48
200
Inca wants to build an enclosure in the shape of a right triangle for her pet penguin. The two perpendicular sides will be made of glass and the hypotenuse will be a wall of ice. If she has 8 meters worth of glass panels, what is the maximum area she can enclose?
8 square meters
300
Factor -2x2+7x+15 completely.
(2x+3)(5-x)
300
Write the equation for this graph in factored form:
4(x-2)2
300
Write (x+5)(x-2) in vertex form.
(x+3/2)2-29/2
300
Usually Zach grades 4 tests per hour. When he works at this pace, he can grade for 6 hours before he is so tired of grading he just can't anymore. He *can* grade faster, but for every test per hour faster that he grades, he runs out of steam and ends up exhausted and bleary-eyed 30 minutes sooner. What is the largest number of tests that Zach can grade in one sitting?
32 tests
400
Factor x5-7x4+3x3-21x2 completely.
x2(x-7)(x2+3)
400
Write the equation for this graph in factored form:
-3(x+1)(x-5)
400
Write ((x-2)3+6x2+4x+8)/x in factored form.
(x+4i)(x-4i)
400
Richard wants to build a terrarium for his pet venus fly trap. It will be essentially a box made of glass with steel rods as edges. The base of the box is a rectangle whose length is twice its width, and Richard has 112 feet of steel rod to use. He wants to maximize the surface area of the box (because photosynthesis). What is the largest surface area he can obtain?
504 square feet
500
Factor 8x4+36x3+54x2+27x completely.
x(2x+3)3
500
Write the equation for this graph in standard form:
x2+10x-4
500
Write (x2+1)2-(x2-2)2 in vertex form.
6x2-3
500
Shelly decides to make the ultimate holiday beverage: peppermint hot chocolate mixed with eggnog. She has a green thermos containing 30 liters of pure hot chocolate, and a red thermos with 12 liters of mixture that is 25% eggnog. She adds x liters of pure eggnog to the green thermos and x liters of pure hot chocolate to the red thermos and now both mixtures taste exactly the same. What is x?
6