How do you find the curve of g(x)=4x-x^2?
I need all of the steps.
Thanks
To find the curve of the function g(x)=4x-x^2, we need to determine the graph of this function. Here are the steps:
Step 1: Start by understanding the general shape of the function.
The function g(x)=4x-x^2 represents a quadratic function, which will have a curved shape. Generally, quadratic functions have a vertex, where the curve reaches its maximum or minimum point.
Step 2: Find the x-coordinate of the vertex.
To find the x-coordinate of the vertex, we can use the formula: x = -b/2a. In this case, a = -1 (coefficient of x^2) and b = 4 (coefficient of x). Plugging these values into the formula, we get x = -(4)/(2*(-1)) = -2.
Step 3: Find the y-coordinate of the vertex.
Substitute the x-coordinate of the vertex into the function g(x) to find the corresponding y-coordinate. In this case, substituting x = -2 into the function g(x) gives g(-2) = 4(-2)-(-2)^2 = -4.
Step 4: Plot the vertex on the coordinate plane.
Using the x and y coordinates obtained, plot the vertex (-2, -4) on the Cartesian plane.
Step 5: Find additional points to complete the graph.
To further determine the shape of the curve, find a few more points by substituting different x-values into the function. For example, substitute x = -3, -1, 0, 1, 2, and 3 into the function g(x) to find the corresponding y-values.
Step 6: Plot the additional points on the coordinate plane.
With the x and y values from step 5, plot the additional points on the Cartesian plane.
Step 7: Connect the plotted points to form a smooth curve.
Using a smooth curve, connect all the plotted points together to form the graph of the function g(x)=4x-x^2.
By following these steps, you should be able to find the curve of the function g(x)=4x-x^2.