Questions: Match each equation in parts (a)-(i) with the sketch of its graph. (a) The correct graph for y=x^2+2 is B. (b) The correct graph for y=x^2-2 is A. (c) The correct correct graph for y=(x+2)^2 is G. (d) The correct graph for y=(x-2)^2 is I.

Match each equation in parts (a)-(i) with the sketch of its graph. (a) The correct graph for y=x^2+2 is B. (b) The correct graph for y=x^2-2 is A. (c) The correct correct graph for y=(x+2)^2 is G. (d) The correct graph for y=(x-2)^2 is I.
Transcript text: Match each equation in parts (a)-(i) with the sketch of its graph. (a) The correct graph for $y=x^{2}+2$ is $B$. (b) The correct graph for $y=x^{2}-2$ is $A$. (c) The correct correct graph for $y=(x+2)^{2}$ is G. (d) The correct graph for $y=(x-2)^{2}$ is I.
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Solution

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Solution Steps

Step 1: Identify the correct graph for \( y = x^2 + 2 \)
  • The graph of \( y = x^2 + 2 \) is a parabola that opens upwards and is shifted 2 units up from the origin.
  • The correct graph is B.
Step 2: Identify the correct graph for \( y = x^2 - 2 \)
  • The graph of \( y = x^2 - 2 \) is a parabola that opens upwards and is shifted 2 units down from the origin.
  • The correct graph is A.
Step 3: Identify the correct graph for \( y = (x + 2)^2 \)
  • The graph of \( y = (x + 2)^2 \) is a parabola that opens upwards and is shifted 2 units to the left from the origin.
  • The correct graph is G.

Final Answer

  1. The correct graph for \( y = x^2 + 2 \) is B.
  2. The correct graph for \( y = x^2 - 2 \) is A.
  3. The correct graph for \( y = (x + 2)^2 \) is G.
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