Question

Matching.

1.
y = 2x² + 4
2.
y = x² - 2x + 1
3.
y = x² - 2x

Answer 1

Do you want these matched to graphs or to descriptions? Below are concise identifying features for each equation you can use to match them.

1) y = 2x^2 + 4
- Vertex: (0, 4)
- Axis of symmetry: x = 0
- y-intercept: (0, 4)
- x-intercepts: none (no real roots)
- Range: y ≥ 4
- Vertex form / transformation: y = 2(x - 0)^2 + 4 — a vertical stretch by 2 and up 4 from y = x^2.

2) y = x^2 - 2x + 1
- Factor / vertex form: (x - 1)^2
- Vertex: (1, 0)
- Axis of symmetry: x = 1
- y-intercept: (0, 1)
- x-intercept: x = 1 (double root)
- Range: y ≥ 0
- Transformation: shift right 1 from y = x^2.

3) y = x^2 - 2x
- Factor: x(x - 2)
- Vertex form: (x - 1)^2 - 1
- Vertex: (1, -1)
- Axis of symmetry: x = 1
- x-intercepts: (0, 0) and (2, 0)
- y-intercept: (0, 0)
- Range: y ≥ -1
- Transformation: shift right 1 and down 1 from y = x^2.

If you have specific graphs or labels to match these to, paste them and I’ll match each equation to the correct graph/description.