Question

Quick Algebra questions please :)

1). Which values best approximate the solutions of -4x^2+11x+2=0?
A). 1.5 and 2.9
B). -0.2 and 2.9
C). 2 and 2.9
D). -0.2 and 2

2). What is the solution set of 4x^2-3=11x?
A). {-3/4,1}
B). {1/4,-3}
C). {-1/4,3}
D). {3/4,-1}

3). What would the graph of g(x)=-(x+2)^2+5 look like?

Answer 1

1. -4x² + 11x + 2 = 0
x = -(11) ± √((11)² - 4(-4)(2))
2(-4)
x = -11 ± √(121 + 32)
-8
x = -11 ± √(153)
-8
x = -11 ± 3√(17)
-8
x = -11 ± 3(4.1)
-8
x = -11 ± 12.3
-8
x = -11 + 12.3 or x = -11 - 12.3
-8 -8
x = 1.3 or x = -23.3
-8 -8
x = -0.1625 or x = 2.9125
x ≈ -0.2 or x ≈ 2.9

The answer is B.

2. 4x² - 3 = 11x
4x² - 11x - 3 = 0
x = -(-11) ± √((-11)² - 4(4)(-3))
2(4)
x = 11 ± √(121 + 48)
8
x = 11 ± √(169)
8
x = 11 ± 13
8
x = 11 + 13 or x = 11 - 13
8 8
x = 24 or x = -2
8 8
x = 3 or x = -0.25

The answer is C.

3. g(x) = -1(x + 2)² + 5
g(x) = -1(x + 2)(x + 2) + 5
g(x) = -1(x(x + 2) + 2(x + 2)) + 5
g(x) = -1(x(x) + x(2) + 2(x) + 2(2)) + 5
g(x) = -1(x² + 2x + 2x + 4) + 5
g(x) = -1(x² + 4x + 4) + 5
g(x) = -1(x²) - 1(4x) - 1(4) + 5
g(x) = -x² - 4x - 4 + 5
g(x) = -x² - 4x + 1