Questions: Find the intercepts and graph the equation by plotting points. y = -x^2 + 9 What are the intercepts? Select the correct choice

Find the intercepts and graph the equation by plotting points. y = -x^2 + 9 What are the intercepts? Select the correct choice
Transcript text: Find the intercepts and graph the equation by plotting points. \[ y=-x^{2}+9 \] What are the intercepts? Select the correct choice
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Solution

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Solution Steps

To find the intercepts of the equation \( y = -x^2 + 9 \), we need to determine where the graph intersects the x-axis and y-axis.

  1. Y-intercept: Set \( x = 0 \) and solve for \( y \).
  2. X-intercepts: Set \( y = 0 \) and solve for \( x \).
Step 1: Find the Y-intercept

To find the y-intercept, we set \( x = 0 \) in the equation \( y = -x^2 + 9 \).

\[ y = -0^2 + 9 = 9 \]

Thus, the y-intercept is \( (0, 9) \).

Step 2: Find the X-intercepts

To find the x-intercepts, we set \( y = 0 \) in the equation \( y = -x^2 + 9 \) and solve for \( x \).

\[ 0 = -x^2 + 9 \]

\[ x^2 = 9 \]

\[ x = \pm 3 \]

Thus, the x-intercepts are \( (3, 0) \) and \( (-3, 0) \).

Final Answer

\[ \boxed{(0, 9), (3, 0), (-3, 0)} \]

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