Which equation represents the function:
moved 2 spaces to the right
and 5 spaces upwards.
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Which equation represents the function:
moved 2 spaces to the right
and 5 spaces upwards.
To solve this problem, we'll start by understanding the transformations required:
Step 1: Apply the horizontal shift 2 units to the right.
To shift a function horizontally, replace with , where is the shift to the right. Thus, we replace with to get:
.
Step 2: Apply the vertical shift 5 units upwards.
To shift a function vertically, add to the function, where is the number of units to shift up. Thus:
.
Combining these transformations, the equation of the transformed function is:
.
This matches the choice labeled as 3. Thus, the correct equation after translating the parabola 2 spaces to the right and 5 spaces upwards is:
.
Find the corresponding algebraic representation of the drawing:
This confuses everyone at first! Think of it this way: to get the same y-value as before, x must be 2 units larger. So when x = 4, we get (4 - 2)² = 2², which gives us the same result that x = 2 used to give.
Use this memory trick: "Horizontal shifts are opposite to what you expect". Moving right uses minus, moving left uses plus. Vertical shifts are intuitive: up uses plus, down uses minus.
The vertex of is always at (h, k). So for , the vertex is at (2, 5).
Yes! You can shift horizontally first, then vertically, or vice versa. The final result will be the same: .
Pick a simple point from the original function, like (0, 0). Apply the shifts: 2 right and 5 up gives you (2, 5). Verify this point satisfies your new equation!
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