To solve the problem step by step, follow these instructions:

Given Function:

$f(x) = 2x^2 - 4x$

You need to find:

1. $f(4.78)$
2. $f(-8.15)$

Step 1: Substitute $x = 4.78$ into the function $f(x)$

The formula is $f(x) = 2x^2 - 4x$. Replace $x$ with $4.78$: $f(4.78) = 2(4.78)^2 - 4(4.78)$

Step 1.1: Calculate $(4.78)^2$

$4.78^2 = 22.8484$

Step 1.2: Multiply $2$ by $22.8484$

$2 \cdot 22.8484 = 45.6968$

Step 1.3: Multiply $4$ by $4.78$

$4 \cdot 4.78 = 19.12$

Step 1.4: Subtract $19.12$ from $45.6968$

$f(4.78) = 45.6968 - 19.12 = 26.5768$

Step 1.5: Round the result to one decimal place

$f(4.78) \approx 26.6$

Step 2: Substitute $x = -8.15$ into the function $f(x)$

Similarly, replace $x$ with $-8.15$: $f(-8.15) = 2(-8.15)^2 - 4(-8.15)$

Step 2.1: Calculate $(-8.15)^2$

$(-8.15)^2 = 66.4225$

Step 2.2: Multiply $2$ by $66.4225$

$2 \cdot 66.4225 = 132.845$

Step 2.3: Multiply $4$ by $-8.15$

$4 \cdot -8.15 = -32.6$

Step 2.4: Subtract $-32.6$ (add $32.6$) to $132.845$

$f(-8.15) = 132.845 + 32.6 = 165.445$

Step 2.5: Round the result to one decimal place

$f(-8.15) \approx 165.4$

Final Answers:

1. $f(4.78) \approx 26.6$
2. $f(-8.15) \approx 165.4$

Would you like me to expand on any step or solve additional problems? Let me know!

Related Questions:

1. How does rounding affect the final answer?
2. Can you find the derivative of $f(x)$?
3. What is the vertex of $f(x) = 2x^2 - 4x$?
4. How do you solve for $x$ when $f(x) = 0$?
5. What happens if $x$ is a fraction?

Tip:

Always perform intermediate calculations with at least 4 decimal places to ensure accuracy before rounding the final result.