Find the x-intercepts
y= x^2-2x-15
answer: x = 2 +/- sqrt 8
I don't get that. Recheck.
To find the x-intercepts of a quadratic equation, we need to set the equation equal to zero and solve for x. In this case, the equation is:
y = x^2 - 2x - 15
To find the x-intercepts, we need to set y equal to zero:
0 = x^2 - 2x - 15
Now, we can try to factor the quadratic equation. However, in this case, it cannot be easily factored. Therefore, we need to use the quadratic formula to find the x-intercepts. The quadratic formula is given as:
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
In our case, we have a = 1, b = -2, and c = -15. Plugging these values into the quadratic formula gives us:
x = (-(-2) +/- sqrt((-2)^2 - 4(1)(-15))) / (2(1))
Simplifying further:
x = (2 +/- sqrt(4 + 60)) / 2
x = (2 +/- sqrt(64)) / 2
x = (2 +/- 8) / 2
Therefore, we have two possible solutions:
x = (2 + 8) / 2 = 10 / 2 = 5
x = (2 - 8) / 2 = -6 / 2 = -3
Hence, the x-intercepts of the equation y = x^2 - 2x - 15 are x = 5 and x = -3.