Final answer:
To factor the quadratic equation y = x^2 - 15x + 36, find two numbers that multiply to 36 and add to -15, which gives y = (x - 3)(x - 12).
Step-by-step explanation:
To factor the quadratic equation y = x^2 - 15x + 36, one must find two numbers that multiply to 36 (the constant term) and add up to -15 (the coefficient of the x term). We are searching for two factors of 36 whose sum is -15. After evaluating the factors of 36, we see that -3 and -12 meet the criteria, as (-3) * (-12) = 36 and (-3) + (-12) = -15. Therefore, the quadratic equation can be factored as:
y = (x - 3)(x - 12)
These represent the points where the graph of the quadratic equation would intersect with the x-axis, indicating the solutions to the equation when y is set to zero.