What are the five points of five point method in quadratic function?

Determine the vertex, and choose two on each side

When selecting points, special points, such as the intersection of X and Y axes and their symmetry points, are generally selected
The vertex determines the position, the other four points determine the opening direction and size of the function image

It's better to have a picture, At 11:00 a.m., an observation post a on an island measured a ship at C, 60 degrees north by East, 12:20 a.m., at B, 60 degrees north by west of the island. At 12:40, the ship arrived at port e, 5000 meters to the west of the island. If the ship always keeps moving at a constant speed, calculate the speed of the ship

Let CD = x, then AC = 2xce ^ 2 = AE ^ 2 + AC ^ 2-2ae * accos angle EAC = 25 + 4x ^ 2-2 * 5 * 2xcos150 degree = 25 + 4x ^ 2 + 10 root sign 3, and CE ^ 2 = de ^ 2 + CD ^ 2 = (5 + radical 3x) ^ 2 + x ^ 2, so 25 + 4x ^ 2 + 10 root sign 3 = (5 + radical 3x) ^

Can the power function image pass through the third quadrant

Some can be as follows: y = x ^ 3, y = x ^ 5

How to draw the image of the - x power function of a minus x power of a?

I can only draw roughly:
Draw one half with point tracing method, and then draw the other half with symmetry (rotation 180 degrees)
For example, for y = 2 ^ X-2 ^ - X:
Because a = 2 > 1, it is relatively simple to draw the right half of the image first. Note that when x is large, the - 2 ^ - x term can be ignored and approximated to an exponential function. Therefore, only the point tracing method is needed, such as the section [0,3], and then the right half is rotated 180 degrees. That is to say, the drawing is very rough, and it seems useless. It is only for reference~
In addition, monotonicity is also very helpful for drawing
y'=ln a *(a^x+a^-x)
So the function monotonically increases (if a > 1) or decreases monotonically (if 0)

How to prove that the power function image is not the fourth quadrant?

When the point in the fourth quadrant is x > 0 and Y0, regardless of the value of N, there is Y > 0,
So it can't cross the fourth quadrant

Use the Geometer's Sketchpad to draw the function image. After inputting the new function, press to make sure that there is no image,,,,, and

Three possibilities
(1) This function does not exist
(2) The position of the function image is outside the display area
(3) This function form is not defined by the Geometer's Sketchpad

How to make function image move along a straight line in Geometer's Sketchpad For example, after drawing the image of the quadratic function y = x ^ 2 with the Geometer's Sketchpad, make it move along y = x in the form of animation

1. Draw a straight line first;
2. Take a point on the straight line;
3. Calculate the abscissa m and ordinate n of point a
4. Draw function y = (x-m) ^ 2 + n
5. Drag point a to see the animation

Why can't the power function image appear in the fourth quadrant? Isn't the function f (x) = - 1 / X in the fourth quadrant?

power function
y=x^a,
When x > 0, y = x ^ a > 0
In the fourth quadrant, x > 0, y

Why does the power function image not cross the fourth quadrant?

That is, when the abscissa of a point is a positive number, its ordinate will never be negative, so the power function is the point that will pass through the fourth quadrant

Why can't the power function image appear in the fourth quadrant

The power function f (x) can be written in the form of the nth power of X, where n is a rational number and can be converted into a / b (a, B are integers); > > (classification discussion:) when n is negative, it is the reciprocal of positive time and has the same sign with it. Therefore, we only consider the case when n is positive, that is, when a and B are both positive

What are the five points of five point method in quadratic function?