Question

При каких значениях t, функция f(x)=3x^2+2tx-(t-1)^2 удовлетворяет условию f(-1)=-2?

Answer 1

3*(-1)^2+2t*(-1)-(t-1)^2=-2
3-2t-(t^2-2t+1)=-2
-2t-t^2+2t-1+5=0 |*(-1)
t^2-4=0
t^2=4
t1=2;
t2=-2.
Ответ: при t=2;-2.

Answer 2

Solving for f(-1) = -2

To find the values of t for which the function f(x) = 3x^2 + 2tx - (t-1)^2 satisfies the condition f(-1) = -2, we can substitute x = -1 into the function and solve for t.

Substituting x = -1 into the function f(x), we get: f(-1) = 3(-1)^2 + 2t(-1) - (t-1)^2 f(-1) = 3 - 2t - (t-1)^2

We need to find the values of t for which f(-1) = -2. Therefore, we have the equation: 3 - 2t - (t-1)^2 = -2

Solving this equation will give us the values of t that satisfy the condition f(-1) = -2.

Solving the Equation

To solve the equation 3 - 2t - (t-1)^2 = -2, we can follow these steps:

1. Expand and simplify the equation. 2. Set the equation equal to 0. 3. Solve for t.

Let's proceed with these steps to find the values of t that satisfy the given condition.

Solution

Expanding and simplifying the equation 3 - 2t - (t-1)^2 = -2, we get: 3 - 2t - (t^2 - 2t + 1) = -2 3 - 2t - t^2 + 2t - 1 = -2 - t^2 + 2 = -2 - t^2 = -2 - 2 - 3 - t^2 = -7 t^2 = 7 t = ±√7

Therefore, the values of t for which the function f(x) = 3x^2 + 2tx - (t-1)^2 satisfies the condition f(-1) = -2 are t = √7 and t = -√7.

Conclusion

The values of t that satisfy the condition f(-1) = -2 for the function f(x) = 3x^2 + 2tx - (t-1)^2 are t = √7 and t = -√7.