Find the corresponding algebraic representation of the drawing:
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Find the corresponding algebraic representation of the drawing:
To solve this problem, let us first note that the labeled point is , which suggests the parabola touches or intersects the y-axis at this point. Without more information indicating horizontal translation, it is reasonable to assume this is the vertex of the parabola, pointing down a simple transformation from to .
Given the simplicity and symmetry (likely no coefficient subtracted or added), this directly translates to a parabola form with only a vertical shift downward.
Therefore, the algebraic representation of the given parabolic drawing is .
The correct choice corresponding to this is .
Which equation represents the function:
\( y=x^2 \)
moved 2 spaces to the right
and 5 spaces upwards.
When the given point has x = 0, it's on the y-axis! This tells us about vertical shifts. The y-coordinate directly shows how far up or down the basic parabola has moved.
Because the point is at (0, -4), not (0, 4)! The negative sign means the parabola is 4 units below the basic curve, so we subtract 4.
From just one point, we assume the simplest transformation. Since (0, -4) is likely the vertex and the parabola appears symmetric, we only need a vertical shift: .
Substitute the given point! For , when x=0: . This matches the point (0, -4) perfectly!
If it opened downward, the equation would be . But looking at the graph, this parabola opens upward, so we keep the positive term.
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