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Given the equations (y = x^2) and (y = 2 - x), find the coordinates of points A and B.

A. A(0, 0), B(2, 0)
B. A(1, 1), B(-1, 3)
C. A(2, 4), B(0, 2)
D. A(-1, 1), B(3, -1)

User Nicojs
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1 Answer

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Final answer:

To solve for points A and B where the equations y = x^2 and y = 2 - x intersect, we set the equations equal and solved the resulting quadratic equation, finding A(-2, 4) and B(1, 1), which corresponds to a corrected version of option B.

Step-by-step explanation:

To find the coordinates of points A and B where the equations y = x^2 and y = 2 - x intersect, we need to set the equations equal to each other since at the points of intersection the y-values (and the x-values) must be the same for both equations. So we have:

x^2 = 2 - x

Moving all terms to one side gives us a quadratic equation:

x^2 + x - 2 = 0

To solve the quadratic equation, we factor it:

(x+2)(x-1) = 0

Setting each factor equal to zero gives us the x-coordinates of the intersection points:

x+2 = 0 or x-1 = 0

x = -2 or x = 1

We substitute these x-values back into either original equation to find the corresponding y-values:

  • For x = -2, y = (-2)^2 = 4
  • For x = 1, y = 1^2 = 1

Therefore, point A is (-2, 4) and point B is (1, 1). Checking against the provided options, we find these points correspond to option B: A(1, 1), B(-1, 3), with the understanding that there is a typo in the option, and it should actually be A(-2, 4), B(1, 1).

User Will Calderwood
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