Question

При каком значении переменной трехчлен:а) у (в квадрате) -4у+9 принимает наименьшее значение?б) -х (в квадрате) +6х-14 принимает наибольшее значение?ответьте и помогита пожалуйста

Answer 1

через дискрименант реши

Answer 2

Finding the Minimum Value of the Expression a) у^2 - 4у + 9

To find the minimum value of the expression у^2 - 4у + 9, we can use the concept of completing the square.

The given expression is a quadratic expression in the variable у. The general form of a quadratic expression is ax^2 + bx + c, where a, b, and c are constants. In this case, a = 1, b = -4, and c = 9.

To find the minimum value, we need to determine the vertex of the quadratic function. The vertex of a quadratic function in the form y = ax^2 + bx + c is given by the coordinates (h, k), where h = -b/2a and k is the minimum value of the function.

For the given expression у^2 - 4у + 9, we have a = 1 and b = -4. Plugging these values into the formula, we can find the x-coordinate of the vertex:

h = -(-4) / (2 * 1) = 4 / 2 = 2

To find the y-coordinate of the vertex, we substitute the x-coordinate (h = 2) into the expression:

у^2 - 4у + 9 = (2)^2 - 4(2) + 9 = 4 - 8 + 9 = 5

Therefore, the minimum value of the expression у^2 - 4у + 9 is 5.

Finding the Maximum Value of the Expression b) -х^2 + 6х - 14

To find the maximum value of the expression -х^2 + 6х - 14, we can again use the concept of completing the square.

The given expression is a quadratic expression in the variable х. The general form of a quadratic expression is ax^2 + bx + c, where a, b, and c are constants. In this case, a = -1, b = 6, and c = -14.

To find the maximum value, we need to determine the vertex of the quadratic function. The vertex of a quadratic function in the form y = ax^2 + bx + c is given by the coordinates (h, k), where h = -b/2a and k is the maximum value of the function.

For the given expression -х^2 + 6х - 14, we have a = -1 and b = 6. Plugging these values into the formula, we can find the x-coordinate of the vertex:

h = -6 / (2 * -1) = 6 / -2 = -3

To find the y-coordinate of the vertex, we substitute the x-coordinate (h = -3) into the expression:

-х^2 + 6х - 14 = -(-3)^2 + 6(-3) - 14 = -9 - 18 - 14 = -41

Therefore, the maximum value of the expression -х^2 + 6х - 14 is -41.

I hope this helps! Let me know if you have any further questions.