Three algebra 2 question

1. The quadratic function f(x) crosses the x-axis at -3 and 1. What are the solutions of f(x)=0?

a. -3 and -1
b. -3 and 1
c. -1 and 3
d. 1 and 3

2. For what values of x does f(x)=x^2+5x+6 reach its minimum value?

a. -3
b. -5/2
c. -2
d. -5

3. Use a quadratic equation to find two real numbers that satisfies the situation. The sum of the two numbers is 12, and their product is -28.

a. 2, 14
b. -2, 14
c. 2, -14
d. no such numbers exist

1) b

2) complete the square
f(x) = x^2 + 5x + 6
f(x) = x^2 + 5x + (5/2)^2 - (5/2)^2 + 6
f(x) = (x + 5/2)^2 - 25/4 + 6
f(x) reaches its minimum at x = -5/2
Answer is (b)

3) x + y = 12
xy = -28
solve the system of equations:
x = -28/y
-28/y + y = 12
-28 + y^2 = 12y
y^2 - 12y - 28 = 0
(y - 14)(y + 2) = 0
y = 14 or y = -2
x = -28/14 = -2 or x = -28/(-2) = 14
The two numbers are -2 and 14. Answer is (b).