If the parabola y = xsquare - 4x + m has only one focus on X axis, then M=

If the parabola y = xsquare - 4x + m has only one focus on X axis, then M=

If there is only one common point with X axis, then the equation y = x & sup2; - 4x + M = 0 has only one solution
So the discriminant is 0
16-4m=0
m=4

The intersection of the straight line y = x-3 with the X axis is a, and the intersection with the Y axis is B. the parabola y = ax & # 178; + BX + C passes through points a, B and m (- 2,5)
(1) Find the analytic formula of the parabola and the coordinates of the vertex M
(2) Let the intersection point of the parabola and the x-axis be C, and find the area of the quadrilateral AMBC

A: (3,0), B: (0, - 3), M: (- 2,5), the solution is C = - 3. B = - 1.5. A = 0.5

The vertex of a parabola is always at (1, - 2), and it passes through (2,3) to find the function relation of quadratic function

From the vertex coordinates, the parabola can be expressed by the vertex formula
y=a﹙x－1﹚²－2
The analytic formula of point (2,3) generation is as follows:
a=5
The analytic expression of this quadratic function is: y = 5 (x-1) &# 178; - 2

An Australian quadratic function problem, a parabola vertex is (Z, - 8), an X-axis intersection is (5,0) Y-axis intersection (0,10), find the value of Z
Please don't ask for the analytic expression of the function first, because I bet with my friends that I can see the Z value without the analytic expression, but I really can't do it

A (Z, - 8), B (5,0), C (0,10) because a is the vertex, so: Yb ya: YC Ya = (XB XA) & sup2;: (XC XA) & sup2;, namely 8:18 = (5-Z) & sup2;: (0-z) & sup2; (5-Z) & sup2; / Z & sup2; = 4 / 9 (Z-5) / z = 2 / 3 or - 2 / 3Z = 3 or 15

The vertex of the parabola y = x ^ 2 + MX + 9 is on the x-axis, and its axis of symmetry is calculated

Since the vertex of the parabola is on the x-axis, there is only one intersection point between the parabola and the x-axis, then the equation x ^ 2 + MX + 9 = 0 has only one real root, that is, m ^ 2-4 * 9 = 0, so m = 6 or - 6, so the symmetry axis of the parabola is x = 3 or - 3

If the vertex coordinates of the parabola whose symmetry axis is parallel to the Y axis are (2,3) and the parabola passes through the point (3,1), then the analytical formula of the parabola is

Let y = a (X-2) ^ 2 + 3
Substituting (3,1) into
a+3=1
a=-2
So y = - 2 (X-2) ^ 2 + 3

Let's know that the axis of symmetry of the parabola is parallel to y, its vertex coordinates are (1,2), and pass through (0, minus 3 / 2),

Because the vertex coordinates are known to be (1,2) and pass a point (0, - 3 / 2), the contrast point of (0, - 3 / 2) is marked as (0,7 / 2), and the answer can be obtained in ax square + BX + C = y. three points determine an equation

It is known that the axis of symmetry is a parabola parallel to the y-axis, passing through points (2,1), (1,2), and one of them is the vertex of the parabola

If (2,1) is a vertex, let the analytic formula be y = a (X-2) 2 + 1, then substitute (1,2) into 2 = a (1-2) 2 + 1, the solution is a = 1, so the analytic formula is y = (X-2) 2 + 1; if (1,2) is a vertex, let the analytic formula be y = a (x-1) 2 + 2, then substitute (2,1) into 1 = a (2-1) 2 + 2, the solution is a = - 1, so the analytic formula is y = (X-2) 2 + 2; so the analytic formula is y = (X-2) 2 + 1 or y = (x-1) 2 + 2

Given that the parabola y = X2 - (2m + 2) X-1 + m has two intersections with the X axis, what is the range of M
It is known that the parabola y = 2x2 - (2m + 2) X-1 + m has two intersections with the x-axis, then what is the value range of M? Sorry, wrong number

（2m+2）^2 -4(m-1)>0
m^2+m+2 >0
The range of constant M is r

In the plane rectangular coordinate system xoy, the intersection of the parabola y = - x2 + X + m2-3m + 2 and the X axis is the origin O and point a respectively, and point B (2, n) is on this parabola
(1) Find the coordinates of point B;

(1) ∵ the parabola y passes through the origin,
∴m2-3m+2=0,
The solution is M1 = 1, M2 = 2,
From the meaning of the title, we know that m ≠ 1,
∴m=2,
The analytical formula of parabola is y = - 1 / 4x2 + 5 / 2x,
∵ point B (2, n) is on the parabola y = - 1 / 4x2 + 5 / 2x,
∴n=4,
The coordinates of point B are (2,4)