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
10.Calculate the real zeros of each quadratic function, if possible.
a.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
10.
a. To calculate the real zeros of f(x) = x^2 - 5x - 14, we need to solve for x when f(x) = 0.
x^2 - 5x - 14 = 0
(x - 7)(x + 2) = 0
x = 7 or x = -2
So, the real zeros of the function f(x) are x = 7 and x = -2.
b. To calculate the real zeros of g(x) = x^2 + 3x - 18, we need to solve for x when g(x) = 0.
x^2 + 3x - 18 = 0
(x + 6)(x - 3) = 0
x = -6 or x = 3
So, the real zeros of the function g(x) are x = -6 and x = 3.
11. Completing the square for the expression x^2 + 12x:
x^2 + 12x = (x + 6)^2 - 36
So the completed square expression is (x + 6)^2 - 36.
12. To determine the roots of the equation x^2 - 8x - 48 = 0 by completing the square:
x^2 - 8x - 48 = 0
(x^2 - 8x) = 48
(x^2 - 8x + 16) = 48 + 16
(x - 4)^2 = 64
Taking the square root of both sides, we get:
x - 4 = ±8
x = 4 ± 8
x = 12 or x = -4
So, the roots of the equation x^2 - 8x - 48 = 0 are x = 12 and x = -4.