y=x2+4x+1
Points: (x, y) and (x, y) Slope: y1-y2/x1-x2
x2+(y-x2/3)2=1
There are two (main) ways to graph this parabola. The first is to simply substitute in values of x, find the corresponding y values and then plot those points and connect the points with a curve. The second way is to 'complete the square' so that we can find where the maximum or minimum occurs and the y-intercept and graph from those two points. This is the process described below. y = -x2 + 8x + 5 y = -(x2 - 8x) + 5 y = -(x2 - 8x + 16 - 16) + 5 y = -(x2 - 8x + 16) + 16 + 5 y = -(x-4)2 + 21 From this we can see that a maximum occurs at (4,21). To find the y-intercept, substitute in x=0, giving y=5. From these two points, we get a pretty good idea of what the graph looks like. If you want more accuracy, substitute in more values of x.
the graph is moved down 6 units
y=x2+4x+1
x2 + y - 49 = 0y = -x2 + 49First, plot the graph of y = -x2, with a vertex (0, 0), then translate it 49 units up. The vertex becomes (0, 49), which is a maximum point (the parabola opens downward).Or make a table to obtain several corresponding y-values for x = -3, -2, -1, 0, 1, 2, 3. Plot the points (x, y), and draw the graph of y = -x + 49.
Points: (x, y) and (x, y) Slope: y1-y2/x1-x2
x2+(y-x2/3)2=1
No translation will invert a quadratic graph.
y = (square root 1- x2) + (cube root x2)
Select a set of value of x in the range over which you wish to draw the graph. For each point, x, calculate x2+1 and then plot the point (x, x2+1) on a coordinate plane. Join these points with a smooth curve.
There are two (main) ways to graph this parabola. The first is to simply substitute in values of x, find the corresponding y values and then plot those points and connect the points with a curve. The second way is to 'complete the square' so that we can find where the maximum or minimum occurs and the y-intercept and graph from those two points. This is the process described below. y = -x2 + 8x + 5 y = -(x2 - 8x) + 5 y = -(x2 - 8x + 16 - 16) + 5 y = -(x2 - 8x + 16) + 16 + 5 y = -(x-4)2 + 21 From this we can see that a maximum occurs at (4,21). To find the y-intercept, substitute in x=0, giving y=5. From these two points, we get a pretty good idea of what the graph looks like. If you want more accuracy, substitute in more values of x.
First, reflect the graph of y = x² in the x-axis (line y = 0) to obtain the graph of y = -x²; then second, shift it 3 units up to obtain the graph of y = -x² + 3.
the graph is moved down 6 units
Interpreting that function as y=x2+2x+1, the graph of this function would be a parabola that opens upward. It would be equivalent to y=(x+1)2. Its vertex would be at (-1,0) and this vertex would be the parabola's only zero.
y = x2 + 2x + 1zeros are:0 = x2 + 2x + 10 = (x + 1)(x + 1)0 = (x + 1)2x = -1So that the graph of the function y = x + 2x + 1 touches the x-axis at x = -1.