If the x value of quadratic function is not equal to zero, how to draw (or mark) its image?

If the x value of quadratic function is not equal to zero, how to draw (or mark) its image?

Quadratic function f (x) = a * (x ^ 2) + BX + C; the title requires that the x value of quadratic function is not equal to zero, the point where x value is equal to zero on the image is the intersection of quadratic function and Y axis, and the coordinate of this point is (0, c); if you want to draw the image of quadratic function, you should draw the image with y on the original complete image
The coordinates of the two focal points are (- 4,0), (4,0) respectively. The sum of the distances from a point P on the ellipse to the two focal points is equal to 10. The standard equation of the ellipse is___ .
∵ the coordinates of the two focal points are (- 4,0), (4,0), ∵ the focal point of the ellipse is on the horizontal axis, and C = 4, ∵ from the definition of the ellipse, we can get 2A = 10, that is, a = 5, ∵ from the relationship of a, B, C, we can get b = 3, ∵ the elliptic equation is & nbsp; X225 + Y29 = 1. So the answer is: X225 + Y29 = 1
Answer the following question without drawing a graph where y equals one-third of x plus four
What question do you want to answer? Y = 1 / 3x + 4 intersects with X axis at a (- 12,0), and intersects with y axis at B (0,4). When x ＞ - 12, y ＞ 0, etc
If the distance between the two focal points of an ellipse is 16 and the distance between a point on the ellipse and the two focal points is 9 and 15 respectively, the standard equation of the ellipse is?
2c=16
C=8
2a=9+15=24
a=12
b=√(a^2-c^2)=√80
So the standard equation for an ellipse is
X ^ 2 / 144 + y ^ 2 / 80 = 1 or Y ^ 2 / 144 + x ^ 2 / 80 = 1
Draw an image of the function y = - 2 / X and observe when - 1
The previous Y > 1 or Y
Given that the distance from the focus of the ellipse to the corresponding guide line is the length of the long half axis, the eccentricity of the ellipse is calculated
Don't use too many words to describe how to do it, but the specific operation process
According to the meaning of the question, we get a & # 178; - C & # 178; = ace = C / A, we get C = EA, we get a & # 178; - E & # 178; a & # 178; = EA & # 178; E & # 178; + E-1 = 0, we get e = (- 1 ± √ 5) / 2, because 0 ＜ e ＜ 1, we get e = (- 1 + √ 5) / 2
The image of function y = a ^ X - A (a > 0, a is not equal to 1) may be
a> 1, the function increases,
Translate y = a ^ x down a unit to get the image of y = a ^ X - A
Then, the image of y = a ^ X - a takes y = - A as the asymptote,
When X -- > - ∞, Y -- > - A, (- a)
The answer upstairs is very good. I hope you can adopt it
Given that the distance from the focus of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) to the corresponding guide line is equal to a, it is urgent to find the eccentricity
It is known that the distance from the focus of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) to the corresponding guide line is equal to a, and the eccentricity of the ellipse is calculated
Right focus (C, 0), right guide x = A & # / C
I.e. a & # / C - C = a
a²-c²=ac
At the same time, divide by a and 178;
1-（c/a）²= c/a
That is E & # 178; + E-1 = 0
The solution is e = (- 1 + √ 5) / 2 or (- 1 - √ 5) / 2
And 0 < e < 1
So e = (- 1 + √ 5) / 2
The image of the function y = a ^ x + 2 - 2 (a > 0, and a is not equal to 1) is always over the fixed point A. if the point a is on the image of the function y = mx-n, where Mn > 0, its minimum value is 1 / M + 2 / n
y=a^(x+2) -2
When x + 2 = 0, i.e. x = - 2, y = 1-2 = - 1
Constant crossing point (- 2, - 1)
Substituting y = mx-n:
-1=-2m-n.
2m+n=1
2m + n > = 2 radical (2Mn), (m, n > 0)
Root sign 2Mn
Why is the sum of the distances from any point on the ellipse to the focus equal to the length of the long half axis
It's all 2A. Can we prove it?
First, the sum of the distances from any point to the focus should be equal to the length of the major axis rather than the length of the major half axis
The distance from the moving point defined by ellipse to two fixed points is 2 A
The equation is x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1
When the point is on the x-axis, that is, y = 0, x = ± a
The length of long axis is 2A
The definition of ellipse...