Question

evaluate $f(x) = -5x^2 + 8x - 2$ at the indicated values
$f(3) = $
$f(1) = $
$f(a + 6) = $

Explanation:

Step1: Evaluate \( f(3) \)

Substitute \( x = 3 \) into \( f(x) = -5x^2 + 8x - 2 \):
\( f(3) = -5(3)^2 + 8(3) - 2 \)
\( = -5(9) + 24 - 2 \)
\( = -45 + 24 - 2 \)
\( = -23 \)

Step2: Evaluate \( f(1) \)

Substitute \( x = 1 \) into \( f(x) = -5x^2 + 8x - 2 \):
\( f(1) = -5(1)^2 + 8(1) - 2 \)
\( = -5 + 8 - 2 \)
\( = 1 \)

Step3: Evaluate \( f(a + 6) \)

Substitute \( x = a + 6 \) into \( f(x) = -5x^2 + 8x - 2 \):
\( f(a + 6) = -5(a + 6)^2 + 8(a + 6) - 2 \)
Expand \( (a + 6)^2 = a^2 + 12a + 36 \):
\( = -5(a^2 + 12a + 36) + 8a + 48 - 2 \)
\( = -5a^2 - 60a - 180 + 8a + 46 \)
Combine like terms:
\( = -5a^2 - 52a - 134 \)

Answer:

\( f(3) = -23 \)
\( f(1) = 1 \)
\( f(a + 6) = -5a^2 - 52a - 134 \)