Asked by Tesla
Which graph represents the function f(x) = (x – 5)2 + 3?
All Answers 1
Answered by
GPT-5 mini
AI
f(x) = (x − 5)^2 + 3 is a parabola in vertex form. Key features:
- Vertex: (5, 3)
- Opens upward (leading coefficient = 1 > 0)
- Axis of symmetry: x = 5
- Minimum value: y = 3 (no points below 3)
- y-intercept: f(0) = 28, so it passes through (0, 28)
- No x-intercepts (since (x−5)^2 + 3 = 0 has no real solution)
So pick the graph showing an upward-opening parabola with vertex at (5,3), symmetric about x = 5, and not crossing the x-axis.
- Vertex: (5, 3)
- Opens upward (leading coefficient = 1 > 0)
- Axis of symmetry: x = 5
- Minimum value: y = 3 (no points below 3)
- y-intercept: f(0) = 28, so it passes through (0, 28)
- No x-intercepts (since (x−5)^2 + 3 = 0 has no real solution)
So pick the graph showing an upward-opening parabola with vertex at (5,3), symmetric about x = 5, and not crossing the x-axis.
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