Answer:
C. F(x) = 2(x-2)²+2
Step-by-step explanation:
This graph was changed by a vertical and horizontal shift because the graph moved over and up
- A vertical shift would be when a constant is added to the output, resulting in the graph moving up or down: y = f(x) + k
- A horizontal shift would be when a constant is added to the input, resulting in the graph moving left or right: y = f(x + h)
With this information we can determine how the graph was transformed
- Looking at the graph, the origin is now at (2,2) instead of (0,0)
- We can see that the graph moved to the right h units, indicating a horizontal shift 2 units to the right
- We can also see that the graph moved up k units, indicating a vertical shift 2 units upward
Our equation for f(x) should be in the form y = a(x + h)² + k
- Substituting in all our known values, we get the equation:
- F(x) = 2(x-2)²+2
Assuming that
is the amount of hours spent doing homework:
Plug in
for
,
That means that since a
value is the test score (because that's what the y-axis is labeled), your predicted test score is a
64.
Complete the square:
<span>y = 3x^2 - 12x + 4 </span>
<span>y = 3(x^2 - 4x) + 4 </span>
<span>y = 3(x^2 - 4x + 4 - 4) + 4 </span>
<span>y = 3(x^2 - 4x + 4) - 12 + 4 </span>
<span>y = 3(x - 2)^2 - 8</span>
