Where does the graph of x2 - x - 2 = y cross the x-axis?
2 and -1
To find where the graph of the equation x^2 - x - 2 = y crosses the x-axis, we need to solve the equation for when y = 0.
Starting with the given equation:
x^2 - x - 2 = y
Replace y with 0:
x^2 - x - 2 = 0
Now, to solve for x, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Comparing the equation to the standard quadratic equation form ax^2 + bx + c = 0, we can identify:
a = 1, b = -1, c = -2
Substituting the values into the quadratic formula:
x = (-(-1) ± √((-1)^2 - 4(1)(-2))) / (2(1))
x = (1 ± √(1 + 8)) / 2
x = (1 ± √9) / 2
x = (1 ± 3) / 2
We have two possible values for x:
1. x = (1 + 3) / 2 = 4 / 2 = 2
2. x = (1 - 3) / 2 = -2 / 2 = -1
Therefore, the graph of the equation x^2 - x - 2 = y crosses the x-axis at x = 2 and x = -1.