Final answer:
To create a quadratic function h with zeros of 5 and 7, use the formula h(x) = k(x - 5)(x - 7) and choose k = 1 for simplicity. This gives the function h(x) = x² - 12x + 35.
Step-by-step explanation:
To write a quadratic function h with zeros of 5 and 7, we need to use the fact that if a function has zeros at x = a and x = b, then the function can be represented by h(x) = k(x - a)(x - b), where k is a non-zero constant coefficient.
In this case, the zeros are 5 and 7, so we have:
h(x) = k(x - 5)(x - 7)
We can choose any non-zero value for k, but common practice is to set k = 1 for simplicity unless given a specific leading coefficient.
Therefore, the quadratic function with these zeros is:
h(x) = (x - 5)(x - 7) = x² - 12x + 35