How to graph this:
Step 0: y=x(x-4)
Step 1: y=x^2-4x
What's next?
Calculator shows vertex at (2,-4)
I asked before, but I'm still stuck. Please help. thanks.
I answered before, by completing the square, and told you why the vertex is at (2, -4).
Why don't you just plot the curve yourself?
I understand why the vertex is there, I just don't understand what you mean by completing the square.
http://www.themathpage.com/alg/complete-the-square.htm#complete
To graph the equation y = x(x-4), or equivalently y = x^2 - 4x, you can follow these steps:
Step 1: Set up a coordinate system (x-axis and y-axis) on a graph paper or a graphing software.
Step 2: Identify key points and the shape of the graph:
- Quadratic equations have a parabolic shape.
- The coefficient of x^2 (which is 1 in this case) determines the general direction of the parabola. A positive coefficient means the parabola opens upward, and a negative coefficient means it opens downward.
- The vertex of the parabola occurs at the minimum or maximum point of the graph.
Step 3: Determine the vertex of the parabola:
- To find the vertex, you can use the formula x = -b/2a, where a and b are the coefficients of x^2 and x, respectively.
- In the equation y = x^2 - 4x, a = 1 and b = -4.
- Substituting these values into the formula, you get x = -(-4)/(2*1) = 2.
Step 4: Find the y-coordinate of the vertex:
- Substitute the x-coordinate of the vertex into the equation y = x^2 - 4x.
- In this case, x = 2. Plugging it into the equation, you get y = 2^2 - 4(2) = 4 - 8 = -4.
- Therefore, the vertex is located at (2, -4).
Step 5: Plot the vertex on the graph by marking the point (2, -4).
Step 6: Determine additional points to plot:
- To further sketch the graph, you can choose some x-values on either side of the vertex and substitute them into the equation to find the corresponding y-values.
- For example, you can substitute x = 0 into y = x^2 - 4x to get y = 0 - 0 = 0.
- Also, substituting x = 4 gives you y = 4^2 - 4(4) = 16 - 16 = 0.
- So, two additional points on the graph are (0, 0) and (4, 0).
Step 7: Connect the plotted points with a smooth curve:
- Use the plotted points (vertex and additional points) to sketch a smooth parabolic curve that passes through them.
By following these steps, you can successfully graph the equation y = x(x-4) or y = x^2 - 4x.