Question

Q2 Complete the table given the function f(x)=-2(x-1)2+5

x
f(x)
-2


-1


0


1


2

Answer 1

Graph the function
f(x) = -2x2 + 5x. What is the y-value that corresponds to the x-value of -1

Answer 2

To complete the table for the function \( f(x) = -2(x-1)^2 + 5 \), we will calculate \( f(x) \) for each given \( x \) value.

1. For \( x = -2 \):
\[
f(-2) = -2(-2-1)^2 + 5 = -2(-3)^2 + 5 = -2(9) + 5 = -18 + 5 = -13
\]

2. For \( x = -1 \):
\[
f(-1) = -2(-1-1)^2 + 5 = -2(-2)^2 + 5 = -2(4) + 5 = -8 + 5 = -3
\]

3. For \( x = 0 \):
\[
f(0) = -2(0-1)^2 + 5 = -2(-1)^2 + 5 = -2(1) + 5 = -2 + 5 = 3
\]

4. For \( x = 1 \):
\[
f(1) = -2(1-1)^2 + 5 = -2(0)^2 + 5 = -2(0) + 5 = 0 + 5 = 5
\]

5. For \( x = 2 \):
\[
f(2) = -2(2-1)^2 + 5 = -2(1)^2 + 5 = -2(1) + 5 = -2 + 5 = 3
\]

Now we can complete the table with the computed values:

| x | f(x) |
|-----|------|
| -2 | -13 |
| -1 | -3 |
| 0 | 3 |
| 1 | 5 |
| 2 | 3 |

This completes the table for the function \( f(x) = -2(x-1)^2 + 5 \).