Questions: Given the function (f(x)=6 x^2+6 x-4). Calculate the following values: (f(0)=-4) (f(2)=32) (f(-2)=8) (f(x+1)=) (f(-x)=)

Transcript text: Given the function $f(x)=6 x^{2}+6 x-4$. Calculate the following values: \[ \begin{array}{l} f(0)=-4 \\ f(2)=32 \\ f(-2)=8 \\ f(x+1)= \\ f(-x)= \end{array} \]

Solution

Solution Steps

Step 1: Calculate $ f(0) $

To find $ f(0) $, substitute $ x = 0 $ into the function $ f(x) = 6x^{2} + 6x - 4 $: \[ f(0) = 6(0)^{2} + 6(0) - 4 = -4 \] Thus, $ f(0) = -4 $.

Step 2: Calculate $ f(2) $

To find $ f(2) $, substitute $ x = 2 $ into the function: \[ f(2) = 6(2)^{2} + 6(2) - 4 = 6(4) + 12 - 4 = 24 + 12 - 4 = 32 \] Thus, $ f(2) = 32 $.

Step 3: Calculate $ f(-2) $

To find $ f(-2) $, substitute $ x = -2 $ into the function: \[ f(-2) = 6(-2)^{2} + 6(-2) - 4 = 6(4) - 12 - 4 = 24 - 12 - 4 = 8 \] Thus, $ f(-2) = 8 $.