Algebra II Chapter 7 Review SOLUTIONS

Remember, you need to have the Quadratic Formula and General Form of a Quadratic Equation memorized for your test!

Here are the solutions for the review (remember that sqrt() is the square root of the number in parentheses, so sqrt(4) = 2):

1) 13 (the degree of a polynomial with more than one variable is the sum of the exponents, which gives us 6+6, 5+7, 6+7, 1+8, and 7+1, and the highest is 6+7 = 13)
2) 4
3) -x^10-2x^6+7x^3; -1
4) cubic (you should have to take differences 3 times)
5) quadratic (degree 2)
6) The parabola crosses the x-axis at -4 and -5, with a stretch factor of 3, which means that from the vertex to the next point on the parabola will be a vertical distance of 3. The parabola should be opening upwards
7) The parabola crosses the x-axis at -3 and -4, with a stretch factor of 3, which means that from the vertex to the next point on the parabola will be a vertical distance of 3. The negative in front of the 3 tells us that the parabola has been reflected across the x-axis, which means it opens downward
8) y = 3(x - 4)^2 + 2
9) x = -5 or x = 1/2
10) x = 0 or x = -2/5
11) (3/8, -3/32)
12) (-1, 0)
13) (2/3, 16/3)
14) (1, 0)
15) (2, 21)
16) h = -16t^2 + 139t + 35; graph is a parabola; t = 8.9 s
17) t = 1/4 s
18) x = 1
19) x = -3
20) x = 6.828 or x = 1.172
21) l = 30
22) -3 + 8i
23) 12 - 14i
24) -8 - 4i
25) -2i, 2i, sqrt(5), -sqrt(5)
26) x = (plus or minus) i*sqrt(5)/4
27) 4x^3 + 8x^2
28) -0.2x^3 + 2.38x^2 - 3.5x - 23.0736
29) x-intercepts: -2, 1; minimum: -4
30) factored form, 2x^2 - 10x + 12, 2(x - 2.5)^2 - 0.5; vertex form, -7x^2 + 14x - 5, use the quadratic formula to get the roots for factored form; general form, (x+1)^2 + 5, use the quadratic formula to get the roots for factored form
31)vertex form, 5x^2 - 20x +17, use the quadratic formula to get the roots for factored form; factored form, -3x^2 + 21x - 36, -3(x - 3.5)^2 + 0.75; general form, (x - 2)^2 + 2, (x - (2+i*sqrt(2))(x + (2 - i*sqrt(2))