Determine the zeros of the quadratic function y= x^2 + 15x + 36.(when listing the smaller zero, remember that negative values are always smaller than positive values.)
To find the zeros of a quadratic function, we set the function equal to zero and solve for x. Setting y = x^2 + 15x + 36 equal to zero, we have:
0 = x^2 + 15x + 36
To factorize this quadratic equation, we need to find two numbers that multiply to 36 and add up to 15 (the coefficient of the x-term). The numbers that satisfy this are 9 and 4:
0 = (x + 9)(x + 4)
Now, we can set each factor equal to zero and solve for x:
x + 9 = 0 or x + 4 = 0
Solving for x in each equation:
x = -9 or x = -4
Therefore, the zeros of the quadratic function y = x^2 + 15x + 36 are -9 and -4. Since negative values are always smaller than positive values, the smaller zero is -9.