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