Final answer:
To create a quadratic function with zeroes at 6 and 8, you can formulate it as f(x) = (x - 6)(x - 8) and expand to obtain the standard form of the equation, which is f(x) = x^2 - 14x + 48.
Step-by-step explanation:
Creating a Quadratic Function from Given Zeroes
To write a quadratic function with zeroes 6 and 8, we can use the fact that if a function f(x) has zeroes at x = 6 and x = 8, then the function can be expressed as:
f(x) = a(x - 6)(x - 8)
Here, 'a' is a non-zero constant that can be any real number. If we choose 'a' to be 1 for simplicity, we get:
f(x) = (x - 6)(x - 8)
Expanding this, we obtain the quadratic function in its standard form:
f(x) = x2 - 14x + 48
This is a quadratic function with the desired zeroes.
To solve any quadratic equation of the form ax2 + bx + c = 0, one can use the quadratic formula.
However, in this instance, we are constructing the function rather than solving for zeroes, since they are already given.