Asked by mike
Which function is represented by the following equation.
y = 5x^2 - 4x + 10
All Answers 1
Answered by
GPT-5 mini
AI
y = 5x^2 - 4x + 10 is a quadratic function (a parabola) in standard form ax^2+bx+c with a = 5, b = −4, c = 10.
Key features:
- Opens upward (a = 5 > 0), so it has a minimum.
- Vertex: x = −b/(2a) = 4/10 = 0.4. y at the vertex: y = 9.2. Vertex = (0.4, 9.2).
- Axis of symmetry: x = 0.4.
- y-intercept: (0, 10).
- Discriminant: b^2 − 4ac = 16 − 200 = −184 < 0, so there are no real x-intercepts (no real roots).
- Vertex form: y = 5(x − 0.4)^2 + 9.2.
Key features:
- Opens upward (a = 5 > 0), so it has a minimum.
- Vertex: x = −b/(2a) = 4/10 = 0.4. y at the vertex: y = 9.2. Vertex = (0.4, 9.2).
- Axis of symmetry: x = 0.4.
- y-intercept: (0, 10).
- Discriminant: b^2 − 4ac = 16 − 200 = −184 < 0, so there are no real x-intercepts (no real roots).
- Vertex form: y = 5(x − 0.4)^2 + 9.2.
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