Finding the Value of f(t+1) When f(x) = 7x^2 - 2

As an excellent high school mathematics teacher, I'm excited to guide you through the process of finding the value of f(t+1) when the function f(x) is given as 7x^2 - 2.

Understanding the Function f(x)

The function f(x) is a quadratic function, which means it can be written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants. In this case, the function is f(x) = 7x^2 - 2.

The key characteristics of this function are:

• a = 7, which means the function is opening upwards.
• b = 0, which means there is no linear term.
• c = -2, which is the y-intercept of the function.

Finding the Value of f(t+1)

To find the value of f(t+1), we need to substitute t+1 into the function f(x).

f(t+1) = 7(t+1)^2 - 2

Now, we can expand the expression: f(t+1) = 7(t^2 + 2t + 1) - 2 f(t+1) = 7t^2 + 14t + 7 - 2 f(t+1) = 7t^2 + 14t + 5

Therefore, the value of f(t+1) is 7t^2 + 14t + 5.

Conclusion

In this article, we've learned how to find the value of f(t+1) when the function f(x) is given as 7x^2 - 2. By understanding the characteristics of the quadratic function and substituting t+1 into the function, we were able to derive the expression 7t^2 + 14t + 5 as the final result.

This skill is crucial for high school mathematics students, as it not only helps them understand the behavior of functions but also prepares them for more advanced topics in calculus and beyond.