Question

Create a graph; then answer the following question.

What are the key points on the graph of y=x2−8x
? Name the vertex, x-intercept(s), and y-intercept.

Answer 1

y = x^2 − 8x

- Vertex: complete the square: y = (x − 4)^2 − 16, so vertex = (4, −16).
- x-intercepts: set y = 0 → x^2 − 8x = x(x − 8) = 0 → x = 0 or x = 8, so (0,0) and (8,0).
- y-intercept: plug x = 0 → y = 0, so y-intercept = (0,0) (same as one x-intercept).

Extras: axis of symmetry x = 4, parabola opens upward, domain (−∞, ∞), range [−16, ∞).