To determine the correct square root equation represented by the graph you're describing, we can analyze the key points based on your description.
From your notes:
- The graph intersects the x-axis at \( x = -9 \). This suggests that when \( y = 0 \), \( x \) must be equal to -9.
- When \( x \) is slightly greater than -9 (like \( x = -8 \)), the graph continues in a curve, and it goes through \( y = 6 \) when \( x \) is positive.
To find the correct equation, we can start with the general form of a square root function:
\[ y = a \sqrt{x - h} + k \]
where \( (h, k) \) represents a horizontal shift left/right and vertical shift up/down, and \( a \) indicates the vertical stretch or compression and direction (up or down).
- Given that the graph intersects the x-axis at \( x = -9 \), we can assume \( h = -9 \). This means the equation would look like \( y = a \sqrt{x + 9} + k \).
- You mentioned the graph has points leading towards \( y = 6 \) as \( x \) approaches some positive value.
Now let's evaluate the options:
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For the option \( y = 2\sqrt{x - 3} \):
- No intersection at \( x = -9 \).
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For the option \( y = 2\sqrt{x + 6} \):
- Intersection would occur at \( x = -6 \).
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For the option \( y = 2\sqrt{x + 9} \):
- This intersects at \( x = -9 \), potentially matching your intersection point. Let’s check. When \( x = -9 \): \[ y = 2\sqrt{-9 + 9} = 2\sqrt{0} = 0 \] This checks out.
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For the option \( y = 2\sqrt{x - 9} \):
- No intersection at \( x = -9 \).
Therefore, the equation that matches your description, specifically where it intersects the x-axis at \( x = -9 \), is:
y = 2√(x + 9)
Thus the answer to the question about which square root equation is represented by the graph is:
y = 2√(x + 9)
3 answers