Question

Не выполняя построения, найдите координаты точек пересечения параболы у = х2 + 4 и прямой х + у = 6.

Answer 1

система

у=х2+4

у=6-х    следует, что

х2+4=6-х

х2+х-2=0

 

по теореме виетта

х+х=-1

х*х=-2 следует х=-2 и х=1

т.к х=-2

у=6-(-2)=8

 

х=1

у=6-1=5

ответ(-2;8)  (1;5)

Answer 2

Finding the Intersection Points of a Parabola and a Line

To find the coordinates of the points of intersection between the parabola y = x^2 + 4 and the line x + y = 6, we can solve the system of equations formed by setting the two equations equal to each other.

The parabola equation is y = x^2 + 4 and the line equation is x + y = 6.

Solving for Intersection Points

To find the intersection points, we can substitute the expression for y from the parabola equation into the line equation:

x + (x^2 + 4) = 6

Solving this equation will give us the x-coordinates of the intersection points. Once we have the x-coordinates, we can substitute them back into the parabola equation to find the corresponding y-coordinates.

Calculating the Intersection Points

By solving the equation x + (x^2 + 4) = 6, we can find the x-coordinates of the intersection points. Let's solve this equation:

x + x^2 + 4 = 6 x^2 + x - 2 = 0

Using the quadratic formula, we can find the solutions for x:

x = (-b ± √(b^2 - 4ac)) / (2a)

Where a = 1, b = 1, and c = -2.

Plugging these values into the quadratic formula will give us the x-coordinates of the intersection points. After finding the x-coordinates, we can substitute them back into the parabola equation to find the corresponding y-coordinates.

Conclusion

The coordinates of the points of intersection between the parabola y = x^2 + 4 and the line x + y = 6 are (-2, 4) and (1, 5).