Math / Algebra

QuestionTranslate each graph as specified below. (a) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=(x+5)^{2}$ . (b) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=x^{2}-4$ .
Part (b)

Studdy Solution

STEP 1

1. We are given the graph of $y = x^2$ .
2. We need to translate this graph to obtain the graph of $y = x^2 - 4$ .

STEP 2

1. Understand the transformation involved.
2. Apply the transformation to the graph of $y = x^2$ .
3. Describe the resulting graph.

STEP 3

Understand the transformation involved: The equation $y = x^2 - 4$ represents a vertical translation of the graph of $y = x^2$ .

STEP 4

Apply the transformation: Subtracting 4 from the function $y = x^2$ shifts the graph downward by 4 units.

STEP 5

Describe the resulting graph: The vertex of the parabola, originally at the origin $(0, 0)$ , moves to $(0, -4)$ . The shape of the parabola remains unchanged, but it is shifted downward.
The graph of $y = x^2 - 4$ is a vertical translation of the graph of $y = x^2$ downward by 4 units.

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QuestionTranslate each graph as specified below. (a) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=(x+5)^{2}$ . (b) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=x^{2}-4$ .
Part (b)

Studdy Solution

STEP 1

1. We are given the graph of $y = x^2$ .
2. We need to translate this graph to obtain the graph of $y = x^2 - 4$ .

STEP 2

1. Understand the transformation involved.
2. Apply the transformation to the graph of $y = x^2$ .
3. Describe the resulting graph.

STEP 3

Understand the transformation involved: The equation $y = x^2 - 4$ represents a vertical translation of the graph of $y = x^2$ .

STEP 4

Apply the transformation: Subtracting 4 from the function $y = x^2$ shifts the graph downward by 4 units.

STEP 5

Describe the resulting graph: The vertex of the parabola, originally at the origin $(0, 0)$ , moves to $(0, -4)$ . The shape of the parabola remains unchanged, but it is shifted downward.
The graph of $y = x^2 - 4$ is a vertical translation of the graph of $y = x^2$ downward by 4 units.

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QuestionTranslate each graph as specified below. (a) The graph of y=x2y=x^{2}y=x2 is shown. Translate it to get the graph of y=(x+5)2y=(x+5)^{2}y=(x+5)2. (b) The graph of y=x2y=x^{2}y=x2 is shown. Translate it to get the graph of y=x2−4y=x^{2}-4y=x2−4.Part (b)

Studdy Solution

STEP 1

1. We are given the graph of y=x2 y = x^2 y=x2.2. We need to translate this graph to obtain the graph of y=x2−4 y = x^2 - 4 y=x2−4.

STEP 2

1. Understand the transformation involved.2. Apply the transformation to the graph of y=x2 y = x^2 y=x2.3. Describe the resulting graph.

STEP 3

Understand the transformation involved: The equation y=x2−4 y = x^2 - 4 y=x2−4 represents a vertical translation of the graph of y=x2 y = x^2 y=x2.

STEP 4

Apply the transformation: Subtracting 4 from the function y=x2 y = x^2 y=x2 shifts the graph downward by 4 units.

STEP 5

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QuestionTranslate each graph as specified below. (a) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=(x+5)^{2}$ . (b) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=x^{2}-4$ .
Part (b)

1. We are given the graph of $y = x^2$ .
2. We need to translate this graph to obtain the graph of $y = x^2 - 4$ .

1. Understand the transformation involved.
2. Apply the transformation to the graph of $y = x^2$ .
3. Describe the resulting graph.

Understand the transformation involved: The equation $y = x^2 - 4$ represents a vertical translation of the graph of $y = x^2$ .

Apply the transformation: Subtracting 4 from the function $y = x^2$ shifts the graph downward by 4 units.