Anna55

05-25-2011, 12:08 PM

The parabola y = –x^2 + 4 has vertex P and intersects the x-axis at A and B.The parabola is translated from its original position so that its vertex moves along the line y = x + 4 to the point Q. In this position, the parabola intersects the x-axis at B and C. Determine the coordinates of C.

The parabola y = –x^2 + 4 has vertex P(0, 4) and intersects the x-axis at A(– 2, 0) and B(2, 0). The intercept B(2, 0) has its pre-image, B? on the parabola y = –x^2 + 4. To find B? , we find the point of intersection of the line passing through B(2, 0), with slope 1, and the parabola y = –x^2 + 4.

The equation of the line is y = x – 2.

Intersection points, x – 2 = –x^2 + 4

x^2+x-6=0

(x+3) (x-2)

Therefore, x = – 3 or x = 2.

For x = – 3, y = – 3 – 2 = – 5. Thus B? has coordinates (– 3, – 5).

If (– 3, – 5)?(2, 0) then the required general translation mpping y = –x^2 + 4 onto the

parabola with vertex Q is (x, y)?(x + 5, y + 5).

I do not understand the things in bold. Can you please explain?

The parabola y = –x^2 + 4 has vertex P(0, 4) and intersects the x-axis at A(– 2, 0) and B(2, 0). The intercept B(2, 0) has its pre-image, B? on the parabola y = –x^2 + 4. To find B? , we find the point of intersection of the line passing through B(2, 0), with slope 1, and the parabola y = –x^2 + 4.

The equation of the line is y = x – 2.

Intersection points, x – 2 = –x^2 + 4

x^2+x-6=0

(x+3) (x-2)

Therefore, x = – 3 or x = 2.

For x = – 3, y = – 3 – 2 = – 5. Thus B? has coordinates (– 3, – 5).

If (– 3, – 5)?(2, 0) then the required general translation mpping y = –x^2 + 4 onto the

parabola with vertex Q is (x, y)?(x + 5, y + 5).

I do not understand the things in bold. Can you please explain?