QQuestionMathematics
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.
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