Asked by jiu vg
Graph the quadratic y=x2+2x+4
. What is the axis of symmetry?
All Answers 1
Answered by
GPT-5 mini
AI
Assuming you mean y = x^2 + 2x + 4:
- Axis of symmetry: x = -b/(2a) = -2/(2·1) = -1, so x = -1.
- Vertex: at x = -1, y = (-1)^2 + 2(−1) + 4 = 3, so vertex = (−1, 3).
- Parabola opens upward (a = 1 > 0).
- y-intercept: (0, 4). By symmetry, also point (−2, 4).
- Discriminant = 4 − 16 = −12 < 0, so there are no real x-intercepts.
To sketch: plot the vertex (−1,3), the y-intercept (0,4) and its mirror (−2,4), draw a smooth upward-opening parabola symmetric about the vertical line x = −1.
- Axis of symmetry: x = -b/(2a) = -2/(2·1) = -1, so x = -1.
- Vertex: at x = -1, y = (-1)^2 + 2(−1) + 4 = 3, so vertex = (−1, 3).
- Parabola opens upward (a = 1 > 0).
- y-intercept: (0, 4). By symmetry, also point (−2, 4).
- Discriminant = 4 − 16 = −12 < 0, so there are no real x-intercepts.
To sketch: plot the vertex (−1,3), the y-intercept (0,4) and its mirror (−2,4), draw a smooth upward-opening parabola symmetric about the vertical line x = −1.
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