\( b = -6a \)
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- We are also given \( b = -6 \). We rewrite the standard form \( f(x) = ax^2 + bx + c \) in vertex form by expanding:
- f(x) = a(x^2 - 6x + 9) - 5 = ax^2 - 6ax + 9a - 5
- Comparing coefficients with \( ax^2 + bx + c \), we identify:
- \( c = 9a - 5 \)
- But we are given \( b = -6 \), so:
- -6a = -6 \Rightarrow a = 1
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