Which of the following quadratic functions does not have zeros of -15 and 6?
To determine which of the given quadratic functions does not have zeros of -15 and 6, we will first examine the general form of a quadratic function: f(x) = ax^2 + bx + c.
Next, we need to find the quadratic function that has the zeros of -15 and 6. For a quadratic function, the zeros are the values of x for which f(x) = 0. Thus, we can set up two equations:
1. (x - (-15))(x - 6) = 0 --> (x + 15)(x - 6) = 0
2. x^2 - 6x + 15x - 90 = 0
3. x^2 + 9x - 90 = 0
Now we have a quadratic function with the desired zeros: f(x) = x^2 + 9x - 90.
Next, we will substitute the coefficients of the quadratic functions given in the options to check which one matches the equation: f(x) = x^2 + 9x - 90.
Option 1: g(x) = x^2 + 16x - 90
Option 2: h(x) = x^2 + 9x + 90
Option 3: i(x) = x^2 + 6x - 90
Comparing the coefficients, we can see that Option 1 (g(x) = x^2 + 16x - 90) and Option 3 (i(x) = x^2 + 6x - 90) are different from the desired quadratic function.
Therefore, the quadratic functions that do not have zeros of -15 and 6 are Option 1 (g(x) = x^2 + 16x - 90) and Option 3 (i(x) = x^2 + 6x - 90).