Question

can someone help me and expalin how to do these five question please and thank you

11. y = ½ x2 +2x – 3
27. 3x2 – 5x = -3x2 + 6
33. x2 + 10x = -8
45. x2 – 6x + 9 = 0
47. (-3,0),(1,4),(-1,6),(2,0)

Answer 1

11. Y = (1/2)x^2 + 2x - 3
Use Quadratic Formula and get:
X = 1.16228, and -5.16228.

27. 3x^2-5x = -3x^2+6
3x^2+3x^2-5x = 6
6x^2 - 5x - 6 = 0
Use the AC method of factoring:
A.C = 6*(-6) = -36 = 3*(-12)=4*(-9).
Choose the pair of factors whose sum =
B or -5: We choose 4, and -9.
6x^2 + (4x-9x) - 6 = 0
Use the 4 terms to form 2 factorable
binomials:

(6x^2+4x) + (-9x-6) = 0
2x(3x+2) + -3(3x+2) = 0
Factor out (3x+2):
(3x+2)(2x-3) = 0

3x + 2 = 0
3x = -2
X = -2/3

2x-3 = 0
2x = 3
X = 3/2.

Solution set: X = -2/3, and 3/2.

33. x^2 + 10x +8 = 0
Use Quadratic Formula and get:
X = -0.87689, and -9.12311

45. x^2 - 6x + 9 = 0
This a perfect square:
(x-3)^2 = (x-3)(x-3) = 0

x-3 = 0
X = 3

x-3 = 0
x = 3

Solution set: X = 3, and 3.

47. I don't know what you want me to
do with this one.