10
If you don't have enough experience to be able to visualize the graph by
looking at the equation, then here's what I suggest:
-- Write the equation:
y2 = -8x
-- Divide each side by -8 :
- 1/8 y2 = x
-- Now take a piece of paper and a pencil. Make a list of 5 or 10 or 15 or 20 numbers
for 'y', some negative and some positive. Then, for each number on the y-list, use the
equation to calculate the corresponding value of 'x', and write that next to it.
-- On the graph, mark a dot at each of the points you calculated. Keep marking more
points until you can see how it's shaping up, and what the curve will look like.
I believe you're going to wind up with a parabola, with its nose at the origin, lying on its
side and opening to the left.
Same way you graph y = -4x - 0.5
The vertex has a minimum value of (-4, -11)
The line 8x-8=0 is the same as x=1. The graph looks like a vertical line that intersects the x axis at x=1.
4y = 8x Divide each side by 4: y = 2x Draw a straight line, through the origin, with a slope of +2 .
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.
2
Same way you graph y = -4x - 0.5
7
The vertex has a minimum value of (-4, -11)
+ 1/8
The line 8x-8=0 is the same as x=1. The graph looks like a vertical line that intersects the x axis at x=1.
4y = 8x Divide each side by 4: y = 2x Draw a straight line, through the origin, with a slope of +2 .
x^2+8x=20 x^2+8x-20=0 (x+10)(x-2)=0 x=-10 and x=2 are the roots (intercepts) (-10,0) and (2,0) are the x-intercepts.
-8x+3y=12 3y = 8x+12 y = (8/3)x + 4 So it will be a line with slope 8/3 and y intercept of 4
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.
y=-10x-4
Y-8x plus 9y equals 10y-8x.