If the image of a linear function y = - 2x + 1 passes through the vertex of the parabola y = x2 + MX + 1 (m ≠ 0), then M=______ ．

If the image of a linear function y = - 2x + 1 passes through the vertex of the parabola y = x2 + MX + 1 (m ≠ 0), then M=______ ．

∵ y = x2 + MX + 1, ∵ vertex coordinates are (- m2, 4 − M24), and the image of the linear function y = - 2x + 1 passes through the vertex of the parabola y = x2 + MX + 1 (m ≠ 0), ∵ 4 − M24 = - 2 × (- m2) + 1, ∵ M = 0 or M = - 4, while m ≠ 0, ∵ M = - 4

It is known that the parabola y = x2-2x + M-1 has only one intersection point with the x-axis and intersects with the y-axis at point A. as shown in the figure, let its vertex be B. (1) find the value of M;
It is known that the parabola y = x2-2x + M-1 has only one intersection point with the x-axis and intersects with the y-axis at point A. as shown in the figure, let its vertex be B
(1) Find the value of M;
(2) Make a parallel line of X axis through a and cross the parabola at point C. prove that △ ABC is an isosceles right triangle;
(3) After the parabola is translated down 4 units, the parabola C ′ is obtained, which is consistent with the left half axis of the x-axis
Intersection at point E, and intersection with y axis at point F, as shown in the figure. Please find point P on the parabola C ', so that △ EFP is
EF is a right triangle with right sides

(1) If there is only one intersection point between the parabola and the x-axis, then the discriminant of X & # 178; - 2x & nbsp; + & nbsp; M-1 = 0 is 0:4-4 (m-1) & nbsp; = & nbsp; 8-4m & nbsp; = & nbsp; 0, & nbsp; M & nbsp; = & nbsp; 2 (2) take X & nbsp; = & nbsp; 0, & nbsp; Y & nbsp; = & nbsp; 1, & nbsp; a (0, & nbsp; n

Given the parabola y = x2-x-2, (1) find the coordinates of the vertex m of the parabola; (2) if the intersection points of the parabola and the X axis are points a and B respectively (point a is on the left side of point B)
It is known that the parabola y = x2-x-2
(1) Find the coordinates of the parabola vertex M;
(2) If the intersection of the parabola and the x-axis is respectively points a and B (point a is on the left side of point B), and intersects with the y-axis at point C, point n is a point on the line segment BM, passing through point n as a vertical line on the x-axis, and the perpendicular foot is point Q. when point n moves on the line segment BM (point n does not coincide with point B and point m), let the length of NQ be t, and the area of quadrangle nqac be s, find the functional relationship between S and T, and the value range of independent variable t;
(3) Is there a point P on the parabola on the right side of the symmetry axis so that △ PAC is a right triangle? If so, find out the coordinates of all qualified points P; if not, explain the reason

This kind of problem you also want to get online to do

What is the absolute value of function y equal to x? Is it a quadratic function? Is its image a parabola?

Y = | x | is a piecewise function
When x ≥ 0, y = x
x