It is known that the image Q of quadratic function y = ax ^ 2 + BX + C has only one intersection point P with X axis, and the intersection point with y axis is B (0,4), and AC = B Find the analytic expression of the quadratic function Translate the image of a function y = - 3x properly to pass through point P. remember that the image is l, and the other intersection of image L and Q is C. please find a point D on the Y axis to make the perimeter of △ CDP shortest

It is known that the image Q of quadratic function y = ax ^ 2 + BX + C has only one intersection point P with X axis, and the intersection point with y axis is B (0,4), and AC = B Find the analytic expression of the quadratic function Translate the image of a function y = - 3x properly to pass through point P. remember that the image is l, and the other intersection of image L and Q is C. please find a point D on the Y axis to make the perimeter of △ CDP shortest

The intersection point B (0,4) with Y-axis is that when x = 0, y = 4, then C = 4 can be obtained by substituting. The first condition is b = 4A
There is only one intersection point, that is, when the parabola is U-shaped and the endpoint of the parabola is on the x-axis, is there a formula for the endpoint of the parabola? When y = 0, X has only one solution, that is, minus B minus the square of B under the root sign minus 4ac, minus B plus the square of B under the root sign minus 4ac is equal, that is, minus 4ac of B is equal to 0. Substituting C = 4, the answer is that the square of B equals 16a and B = 4A, and B = plus minus 4, a = 1, AC = B, Then B can't be equal to - 4. There are two kinds of analytic expressions: y = x ^ 2 + 4x + 4. When the parabola is a horizontal U-shape, is this possible? I don't remember. I graduated too long. Don't blame me for my mistake
The first equation is expressed analytically, then the intersection point with X axis is p (- 2,0), and the analytic expression of L is y = - 3 (x + 2)
If only, the two intersections will come out, that is, P (- 2,0) and C (- 5,9)
The shortest perimeter is to find out a point d to make it the shortest distance to the sum of P and C. I don't remember what conditions this should meet, but I remember that there was such a problem before. The shortest distance between two points and a line is typically compared to a highway. Now you just learn here. You should be able to turn over a book and calculate the last step by yourself
Well, come to think of it, the answer to 1224329606 is the positive solution. This is the symmetry point based on the physical specular reflection. I remember wrong,