Question

Как найти координаты точек пересечения не выполняя построения y = 4x2(квадрат) и y = 2 - 7x.

Answer 1

надо приравнять 4х²=2-7х   получим уравнение 4х²+7х-2=0   Д=7²-4·4·(-2)=49+32=81

х1=(-7+9)/2·4=2/8=1/4   у1=4·(1/4)²=4·1/16=1/4

х2=(-7-9)/2·4=-16/8=-2   у2=4·(-2)²=4·4=16

ответ (1/4;1/4)   и   (-2;16)

Answer 2

Finding the Coordinates of Intersection Points Without Graphing

To find the coordinates of the intersection points of the given equations y = 4x^2 and y = 2 - 7x, we can solve the system of equations by setting them equal to each other:

1. Set the two equations equal to each other: - 4x^2 = 2 - 7x

2. Rearrange the equation into standard form: - 4x^2 + 7x - 2 = 0

3. Solve for x using the quadratic formula: - x = (-b ± √(b^2 - 4ac)) / (2a)

4. Substitute the values of a, b, and c into the quadratic formula and solve for x.

Let's calculate the values of x and then find the corresponding y-values.

Calculating the Values of x

Using the quadratic formula, we can calculate the values of x:

x = (-7 ± √(7^2 - 4*4*(-2))) / (2*4)

x = (-7 ± √(49 + 32)) / 8

x = (-7 ± √81) / 8

x = (-7 ± 9) / 8

This gives us two potential values for x.

Finding the Corresponding y-Values

Now that we have the values of x, we can find the corresponding y-values by substituting these x-values into either of the original equations.

For the equation y = 4x^2: - When x = (-7 + 9) / 8, y = 4 * ((-7 + 9) / 8)^2 - When x = (-7 - 9) / 8, y = 4 * ((-7 - 9) / 8)^2

By calculating these values, we can find the coordinates of the intersection points.

This approach will help us find the coordinates of the intersection points without graphing the equations.

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