Question - Quadratic Function Table Completion
Solution:
Para completar la tabla, sustituiremos cada valor de \( x \) en la función cuadrática \( f(x) = x^2 - 8x + 7 \) y resolveremos para \( f(x) \).
Para \( x = 0 \):
\( f(0) = (0)^2 - 8(0) + 7 = 0 - 0 + 7 = 7 \)Para \( x = 1 \):
\( f(1) = (1)^2 - 8(1) + 7 = 1 - 8 + 7 = 0 \)Para \( x = 2 \):
\( f(2) = (2)^2 - 8(2) + 7 = 4 - 16 + 7 = -5 \)Para \( x = 3 \):
\( f(3) = (3)^2 - 8(3) + 7 = 9 - 24 + 7 = -8 \)Para \( x = 4 \):
\( f(4) = (4)^2 - 8(4) + 7 = 16 - 32 + 7 = -9 \)Para \( x = 5 \):
\( f(5) = (5)^2 - 8(5) + 7 = 25 - 40 + 7 = -8 \)Para \( x = 6 \):
\( f(6) = (6)^2 - 8(6) + 7 = 36 - 48 + 7 = -5 \)La tabla completa sería:
\[ \begin{array}{c|c} x & f(x) \\ \hline 0 & 7 \\ 1 & 0 \\ 2 & -5 \\ 3 & -8 \\ 4 & -9 \\ 5 & -8 \\ 6 & -5 \\ 7 & 0 \\ 8 & 7 \\ \end{array} \]
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