Question

Задана функция y = −4x² + 8x + c. Определите значение c, при котором наибольшее значение функции равно 7.Решение записывайте подробно.

Answer 1

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Answer 2

Ответ:

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Answer 3

Problem Analysis

We are given a function y = -4x² + 8x + c and we need to determine the value of c such that the maximum value of the function is equal to 7.

Solution

To find the maximum value of the function, we need to find the vertex of the parabola represented by the function. The vertex of a parabola in the form y = ax² + bx + c is given by the formula:

x = -b / (2a)

In our case, a = -4 and b = 8. Substituting these values into the formula, we get:

x = -8 / (2 * -4) x = -8 / -8 x = 1

Now, we substitute this value of x back into the original function to find the corresponding y-coordinate of the vertex:

y = -4(1)² + 8(1) + c y = -4 + 8 + c y = 4 + c

Since we want the maximum value of the function to be equal to 7, we set y = 7 and solve for c:

4 + c = 7 c = 7 - 4 c = 3

Therefore, the value of c that makes the maximum value of the function equal to 7 is c = 3.

Conclusion

The value of c that makes the maximum value of the function y = -4x² + 8x + c equal to 7 is c = 3.