Question

what are the key points on the graph of y=x^2-8x

Answer 1

The key points on the graph of y = x^2 - 8x are as follows:

1. Intercepts:
- x-intercepts: To find the x-intercepts, set y = 0 and solve for x. So, 0 = x^2 - 8x. Factoring, we get x(x - 8) = 0. This gives us two x-intercepts: x = 0 and x = 8.
- y-intercept: To find the y-intercept, set x = 0. So, y = (0)^2 - 8(0) = 0. Hence, the y-intercept is 0.

2. Vertex: The vertex of the parabola can be found using the formula x = -b / (2a), where the equation is in the form y = ax^2 + bx + c. Comparing it with the given equation y = x^2 - 8x, we have a = 1 and b = -8. Therefore, x = -(-8) / (2*1) = 4. Substituting x = 4 into the equation gives us y = (4)^2 - 8(4) = 16 - 32 = -16. Thus, the vertex is (4, -16).

3. Axis of symmetry: The axis of symmetry is a vertical line passing through the vertex. In this case, the axis of symmetry is x = 4.

4. Shape: Since the coefficient of x^2 is positive, the parabola opens upward.

5. Symmetry: The graph is symmetric with respect to the axis of symmetry (x = 4).

Please note that these are the main key points, and there may be other important features depending on the context or requirements of the problem.