Question

question 2
if $f(x) = 2x^2 - 5x + 3$, what is $f(-3)$?

• 0
• 36
• 24
• 13

Explanation:

Step1: Substitute \( x = -3 \) into \( f(x) \)

\( f(-3) = 2(-3)^3 - 5(-3) + 3 \)

Step2: Calculate each term

First, calculate \( (-3)^3 = -27 \), so \( 2(-3)^3 = 2\times(-27) = -54 \)
Then, \( -5(-3) = 15 \)

Step3: Sum the terms

\( f(-3) = -54 + 15 + 3 \)
\( f(-3) = -54 + 18 \)
\( f(-3) = -36 \)? Wait, no, wait, maybe I made a mistake. Wait, let's recalculate:

Wait, \( (-3)^3 = -27 \), so \( 2\times(-27) = -54 \)
\( -5\times(-3) = 15 \)
Then \( -54 + 15 + 3 = (-54 + 15) + 3 = -39 + 3 = -36 \)? But the options are 0, 36, 24, 13. Wait, maybe the function is \( f(x) = 2x^2 - 5x + 3 \)? Because if it's \( x^2 \) instead of \( x^3 \), let's check:

If \( f(x) = 2x^2 - 5x + 3 \), then \( f(-3) = 2(-3)^2 - 5(-3) + 3 \)
\( (-3)^2 = 9 \), so \( 2\times9 = 18 \)
\( -5\times(-3) = 15 \)
Then \( 18 + 15 + 3 = 36 \)
Ah, maybe the original function was \( 2x^2 \) instead of \( 2x^3 \). So assuming that, let's redo:

Step1: Substitute \( x = -3 \) into \( f(x) = 2x^2 - 5x + 3 \)

\( f(-3) = 2(-3)^2 - 5(-3) + 3 \)

Step2: Calculate each term

\( (-3)^2 = 9 \), so \( 2\times9 = 18 \)
\( -5\times(-3) = 15 \)

Step3: Sum the terms

\( f(-3) = 18 + 15 + 3 = 36 \)

Answer:

36 (assuming the function is \( f(x) = 2x^2 - 5x + 3 \) instead of \( 2x^3 - 5x + 3 \), as the cubic version gives a result not in the options)