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QuestionMathematics

Write a quadratic function f whose zeros are 3 and 5.
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Step 1:
I'll solve this step by step using the precise LaTeX formatting guidelines you specified:

Step 2:
: Understand the Problem

This means the function will pass through the points $$(3, 0)$$ and $$(5, 0)$$.
x = 5.

Step 3:
: General Form of Quadratic Function

A quadratic function has the standard form $$f(x) = ax^{2} + bx + c$$, where $$a \neq 0$$.

Step 4:
: Use Zero Conditions

f(x) = a(x - 3)(x - 5)
Since the zeros are 3 and 5, we can factor the function as:

Step 5:
: Expand the Factored Form

f(x) = a(x^{2} - 8x + 15)

Step 6:
: Choose a Value for a

We can choose $$a = 1$$ for simplicity:
f(x) = x^{2} - 8x + 15

Final Answer

f(x) = x^{2} - 8x + 15 is a quadratic function with zeros at 3 and 5.