Answer:
To factor the quadratic equation y = x^2 - 8x - 9, we need to find two numbers that multiply to give -9 and add to give -8 (the coefficient of the x term).
We can start by looking for two factors of -9 that add up to -8. The only pair of factors that works are -9 and 1. This is because (-9) + 1 = -8, and (-9) times 1 is -9.
Now we can use these factors to express the middle term of the quadratic in terms of two separate terms that can be factored by grouping. We can do this by splitting the -8x term into -9x + x:
y = x^2 - 9x + x - 9
Now we can group the first two terms together and the last two terms together:
y = (x^2 - 9x) + (x - 9)
We can factor out x from the first group, and factor out -9 from the second group:
y = x(x - 9) + (-9)(x - 9)
Finally, we can factor out the common factor of (x - 9):
y = (x - 9)(x - 1)
Therefore, the factor form of the quadratic equation y = x^2 - 8x - 9 is (x - 9)(x - 1).