Which of the following values are zeros for the function below? Select all that apply.
g(x) = (x^2+4x-12)(x-3)
-6
-3
-2
0
2
3
6
To find the zeros of the function, we set g(x) equal to 0 and solve for x:
g(x) = 0
(x^2 + 4x - 12)(x - 3) = 0
The zeros occur where either x^2 + 4x - 12 = 0 or x - 3 = 0.
Solving x^2 + 4x - 12 = 0:
(x + 6)(x - 2) = 0
x = -6 or x = 2
Solving x - 3 = 0:
x = 3
Therefore, the zeros for the function g(x) are x = -6, 2, and 3.
Ms. Scarborough solved x2 + 6x - 7 by completing the square in the table below. Identify the missing steps.
To complete the square for the quadratic x^2 + 6x - 7:
1. Start with the equation x^2 + 6x - 7 = 0.
2. Add the square of half the coefficient of x to both sides:
x^2 + 6x + (6/2)^2 - 7 = (6/2)^2
x^2 + 6x + 9 = 7 + 9
3. Factor the perfect square trinomial:
(x + 3)^2 = 16
4. Take the square root of both sides:
x + 3 = ±√16
5. Solve for x:
x = -3 ± 4
x = -3 + 4 or x = -3 - 4
x = 1 or x = -7
Missing steps or calculations in the table:
- The completion of the square by adding (6/2)^2 to both sides.
- Factoring the perfect square trinomial (x + 3)^2 = 16.