Given the parabola y = x2-mx + m-2, what is the number of intersections between the parabola and X axis

Discriminant delta = B ^ 2-4 * a * C = m ^ 2-4m + 8 = (M + 2) ^ 2 + 4 > 0
The opening is upward, so there are two intersections

If the vertex coordinates of the parabola y = AX2 + 2x + C are (2,3), then a = a_ ，c= _ ．

∵ y = AX2 + 2x + C, ∵ B2A = - 22a = - 1A, 4ac-b24a = 4ac-44a = ac-1a, ∵ vertex coordinates are (2,3), ∵ 1A = 2ac-1a = 3, the solution is a = - 12C = 1, so the answer is - 12,1

When the vertex of parabola y = ax-2x + C is known (1, - 1), what are the values of a and C

The vertex of ∵ parabola is (1, - 1) ∵ its axis of symmetry is a straight line x = 1 ∵ - B / 2A = 1, that is, 2A = - B → a = - B / 2 ∵ B = - 2 ∵ a = 1 ∵ y = x-2x + C. substituting (1, - 1) into - 1 = 1-2 + C, the solution is C = 0, then the analytical formula of parabola is y = x-2x

The vertex of the square + 2x + C of the parabola y = ax is (1 / 3,1) to find a, C

Vertex coordinate formula (- B / 2a, 4ac-b ^ 2 / 4A)
-b/2a=-2/2a=1/3 a=-3
4ac-b^2/4a=1
( -12c-4)/-12=1 c=2/3

It is known that the vertex of parabola y = ax * + C is (0,2), and its shape and opening direction are the same as y = - 1 / 2x *
(1) Finding the value of a and C
(2) How to translate the image of quadratic function to the origin

The same shape and opening direction means a = - 1 / 2
When x = 0, y = 2, C is 2
y=-1/2x*+2

As shown in the figure, it is known that the other intersection of the parabola y = - 2x2 + 4x passing through the origin and the X axis is a. now it is translated to the right by M (M & gt; 0) units. The resulting parabola intersects with the X axis at C and D, and intersects with the original parabola at p. (1) find the coordinates of point a, and judge its shape when △ PCA exists (no reasoning is required); (2) whether there are two equal line segments on the X axis? If it exists, please find them one by one and write down their lengths (which can be expressed by the formula containing m); if it does not exist, please explain the reason; (3) let the area of △ CDP be s, and find the relationship between S and m

(1) Let - 2x2 + 4x = 0, we obtain that the coordinates of point a are (2,0) △ PCA and isosceles triangle. (2) exist. OC = ad = m, OA = CD = 2. (3) as shown in the figure, when 0 & lt; M & lt; 2, make pH ⊥ X axis at h, let P (XP, YP) ∵ a (2,0), C (m, 0) ≁ AC = 2-m, ≁ ch = ac2 = 2-m

It is known that the intersection of the parabola y = - X & # 178; + (6-2k) x + 2k-1 and the Y axis is located above (0,5), so the value range of K can be obtained

It can be seen from the meaning that when x = 0, the value of quadratic function y = - x ^ 2 + (6-2k) x + 2k-1 y should be > 5
So 2k-1 > 5, so k > 3

The coordinates of the intersection point of the parabola y = 2x & # 178; - 5x + 3 and the Y-axis and the x-axis are?
There is also want to know the specific steps, convenient to do later.
It must be right

Parabola y = 2x & # 178; - 5x + 3
When x = 0, y = 3
So the coordinates of the intersection of the parabola and the y-axis are (0,3)
When y = 0, there is an equation
2x²-5x+3=0
(x-1)(2x-3)=0
X-1 = 0 or 2x-3 = 0
X = 1 or x = 3 / 2
Therefore, the coordinates of the intersection of the parabola and the x-axis are (1,0) and (3 / 2,0)

It is known that the parabola y = 2 (K + 1) x & # 178; + 4kx + 2k-3, when k is_____ The parabola intersects the X axis at two points

y=2(k+1)x²+4kx+2k-3
If it intersects the X axis at two points, then
Δ=16k²-8(k+1)(2k-3)>0
Sorting: 2K & # 178; - (2k & # 178; - K-3) > 0
That is K + 3 > 0, k > - 3
So when k > - 3, the parabola intersects the X axis at two points

The square of the parabola y = 4x, join the right triangle in the parabola, and find m at the origin line AB: y = x + M

To solve this problem, use the general mathematical method. What do you think of this solution!
Because the parabola y ^ 2 = 4x (domain x > 0) inscribes the right triangle at the origin line AB: y = x + M
So you take the line into the parabola and you get the value of X
So there is: x ^ 2 + (2m-4) x + m ^ 2 = 0 and there are two solutions, so the discriminant (2m-4) ^ 2-4m ^ 2 > 0
The range of M is: M

Given the parabola y = x2-mx + m-2, what is the number of intersections between the parabola and X axis