Question

Given that the zeros of a quadratic function are 3 and 7, what is the standard form of the quadratic function?

1) f(x) = x² - 7x + 21
2) f(x) = x² - 10x + 21
3) f(x) = x² - 7x - 21
4) f(x) = x² - 10x - 21

Answer 1

The standard form of the quadratic function with zeros at 3 and 7 is f(x) = x² - 10x + 21.

Step-by-step explanation:

The zeros of a quadratic function are the values of x where the function equals zero. In this case, the zeros are 3 and 7. To find the standard form of the quadratic function, we can use the fact that the zeros are also the solutions when the function equals zero. So, if the zeros are 3 and 7, then the factors of the quadratic function are (x - 3) and (x - 7). Multiplying these factors gives us the quadratic function in factored form: f(x) = (x - 3)(x - 7). Expanding this expression gives us the standard form of the quadratic function: f(x) = x² - 10x + 21.