Final answer:
A quadratic function with zeros -3 and -7 can be written as f(x) = (x + 3)(x + 7), which expands to f(x) = x^2 + 10x + 21.
Step-by-step explanation:
To write a quadratic function f whose zeros are -3 and -7, you can start by using the fact that if x = -3 and x = -7 are zeros of the quadratic, then the function can be represented as f(x) = a(x + 3)(x + 7), where a is a non-zero constant. The zeros indicate the values for which the function equals to zero, and since these are the points where the graph of the function intersects the x-axis, they are also called x-intercepts.
To find a, we need more information, like another point on the graph. However, if no additional points are given, you can choose any non-zero value for a.
For simplicity, we can choose a = 1.
Therefore, the quadratic function can be written as f(x) = (x + 3)(x + 7) which expands to f(x) = x^2 + 10x + 21.