Question

ПОЖАЛУЙСТА ПОМОГИТЕПостроить график функцииy= -x^2+2x+3По графику выяснить:1) при каких значения х функция принимает положительные [отрицательные] значения2)при каких значениях х функция убывает [возрастает] 3) при каких значения х функция принимает наименьшее [наибольшее] значение и найти это значение.

Answer 1

Решение во вложении..!

 

Answer 2

Graph of the Function y = -x^2 + 2x + 3

To understand the behavior of the function y = -x^2 + 2x + 3 and answer the given questions, let's first analyze the graph of the function.

The graph of the function y = -x^2 + 2x + 3 is a downward-opening parabola because the coefficient of x^2 is negative. The vertex of the parabola can be found using the formula for the x-coordinate of the vertex: x = -b / (2a), where a is the coefficient of x^2 and b is the coefficient of x.

1) Values of x for Positive and Negative y

The function will have positive y-values when it is above the x-axis and negative y-values when it is below the x-axis. We can find the x-values where the function crosses the x-axis to determine when it changes from positive to negative and vice versa.

The x-intercepts can be found by setting y = 0 and solving for x using the quadratic formula. The discriminant of the quadratic formula will determine the nature of the roots.

2) Increasing and Decreasing Behavior

The function will be increasing when its slope is positive and decreasing when its slope is negative. We can find the critical points of the function and analyze the slope of the function around these points to determine where it is increasing or decreasing.

3) Minimum and Maximum Values

The minimum or maximum value of the function occurs at the vertex of the parabola. By analyzing the vertex, we can determine the x-value at which the function takes its minimum or maximum value and find this value of the function.

Let's proceed to find the specific values of x and corresponding y-values based on the analysis of the graph and the function.

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