A curve has equation y= 2 + x - x^2. Find coordinates of 3 unknown points on the line. 1st point is at negative x, y value. 2nd point is at x=0 and y is positive. 3rd value is at y=o and x is positive.
y(-x) = 2 + (-x) - (-x)^2 = 2-x-x^2
(0,2)
(2,0)
If my digit in my tens column is7 more than 2, and the digit in my Inés column 9 less than 10. What number am I?
To find the coordinates of the three unknown points on the curve, let's go step by step.
1. The first point is at negative x and y value. To find this point, substitute a negative value for x. Let's say we choose x = -1. Substitute this value into the equation of the curve:
y = 2 + x - x^2
y = 2 + (-1) - (-1)^2
y = 2 - 1 - 1
y = 0
Therefore, the first point is (-1, 0).
2. The second point is at x = 0 and y is positive. To find this point, substitute x = 0 into the equation:
y = 2 + x - x^2
y = 2 + 0 - 0^2
y = 2
Therefore, the second point is (0, 2).
3. The third point is at y = 0 and x is positive. To find this point, substitute y = 0 into the equation:
0 = 2 + x - x^2
This equation is a quadratic equation, and we need to solve it to find the value(s) of x. One way to solve it is by factoring or using the quadratic formula, but in this case, let's use factoring. Rearrange the equation:
x^2 - x - 2 = 0
Factor this equation:
(x - 2)(x + 1) = 0
Setting each factor equal to zero, we have:
x - 2 = 0 --> x = 2
x + 1 = 0 --> x = -1
Therefore, the third point can have two possibilities: (2, 0) and (-1, 0).
To summarize, the coordinates of the three unknown points on the curve are:
1. (-1, 0)
2. (0, 2)
3. (2, 0) OR (-1, 0)