SOLVING QUADRATIC
EQUATIONS
9. Write a factored form for each trinomial.
a. x2 + 12x + 35
x2 - 12х + 35
x2 + 12x - 35
x2 - 12х - 35
b. 2x2 - 9x + 9
2x2 - 3x -9
2x2 + 3x - 9
2x2 + 9x +9
Calculate the real zeros of each quadratic function, if possible.
1. f(x) = x2 - 5х - 14
b. g (x) = x2 + 3x - 18
11. Use the model to complete the square for the expression x2 + 12x. Factor the resulting expression.
12. Determine the roots of the equation x2 - 8x - 48 = 0 by completing the square
1. To find the real zeros of f(x) = x2 - 5x - 14, we can factor the quadratic equation:
f(x) = (x - 7)(x + 2)
Setting each factor to zero:
x - 7 = 0
x = 7
x + 2 = 0
x = -2
The real zeros of the equation are x = 7 and x = -2.
b. To find the real zeros of g(x) = x2 + 3x - 18, we can factor the quadratic equation:
g(x) = (x + 6)(x - 3)
Setting each factor to zero:
x + 6 = 0
x = -6
x - 3 = 0
x = 3
The real zeros of the equation are x = -6 and x = 3.
11. Completing the square for x2 + 12x:
x2 + 12x = (x + 6)2 - 36
12. To solve x2 - 8x - 48 = 0 by completing the square:
x2 - 8x = (x - 4)2 - 16
Adding 16 to both sides:
(x - 4)2 = 64
Taking the square root of both sides:
x - 4 = ±8
x = 4 ± 8
x = 12 or x = -4
The roots of the equation are x = 12 and x = -4.