QuestionTranslate each graph as specified below. (a) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=x^{2}+1$ . (b) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=(x+5)^{2}$ .

Studdy Solution

STEP 1

1. The original graph is $y = x^2$ .
2. We need to apply vertical and horizontal translations to the graph of $y = x^2$ .

STEP 2

1. Translate the graph vertically for part (a).
2. Translate the graph horizontally for part (b).

STEP 3

To translate the graph of $y = x^2$ to $y = x^2 + 1$ , recognize that this is a vertical translation.
The transformation $y = x^2 + 1$ indicates a shift upwards by 1 unit.

STEP 4

To translate the graph of $y = x^2$ to $y = (x+5)^2$ , recognize that this is a horizontal translation.
The transformation $y = (x+5)^2$ indicates a shift to the left by 5 units.
The translations are: (a) Shift the graph of $y = x^2$ up by 1 unit to obtain $y = x^2 + 1$ . (b) Shift the graph of $y = x^2$ left by 5 units to obtain $y = (x+5)^2$ .

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