Question

Не выполняя построений найдите координаты точек пересечения параболы y=x^2+x+2 и прямой y=2x+2помогите пожалуйста решить.

Answer 1

Решение во вложении.

Answer 2

Finding the Intersection Points of a Parabola and a Line

To find the coordinates of the intersection points between the parabola y = x^2 + x + 2 and the line y = 2x + 2, we can set the two equations equal to each other and solve for the values of x.

Let's proceed with the calculation:

1. Set the equations equal to each other: x^2 + x + 2 = 2x + 2

2. Rearrange the equation to bring all terms to one side: x^2 - x - 2 = 0

3. Solve the quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, we can factor the equation: (x - 1)(x + 2) = 0

4. Set each factor equal to zero and solve for x: - x - 1 = 0 --> x = 1 - x + 2 = 0 --> x = -2

5. Substitute the values of x back into either the parabola or the line equation to find the corresponding y-values: - For x = 1: - Using the parabola equation: y = (1)^2 + (1) + 2 = 4 - Using the line equation: y = 2(1) + 2 = 4 Therefore, the first intersection point is (1, 4).

- For x = -2: - Using the parabola equation: y = (-2)^2 + (-2) + 2 = 6 - Using the line equation: y = 2(-2) + 2 = -2 Therefore, the second intersection point is (-2, 6).

Therefore, the coordinates of the intersection points between the parabola y = x^2 + x + 2 and the line y = 2x + 2 are (1, 4) and (-2, 6).