Application of quadratic function in junior high school mathematics A mall bought a commodity at the price of 30 yuan per piece. In the trial sale, it was found that the daily sales volume m (pieces) of this commodity and the sales price x (yuan) of each piece satisfy a linear function: M = 162-3x (1) Write the functional relationship between the daily sales profit y and the sales price X 2) If shopping malls want to get bigger sales profit every day, what is the most appropriate price for each commodity? What is the maximum sales profit?

Application of quadratic function in junior high school mathematics A mall bought a commodity at the price of 30 yuan per piece. In the trial sale, it was found that the daily sales volume m (pieces) of this commodity and the sales price x (yuan) of each piece satisfy a linear function: M = 162-3x (1) Write the functional relationship between the daily sales profit y and the sales price X 2) If shopping malls want to get bigger sales profit every day, what is the most appropriate price for each commodity? What is the maximum sales profit?

The sales profit of each commodity is (X-30) yuan
So the sales profit of M pieces is
y=m（x-30）=（162-3x）（x-30）,
Y = - 3x2 + 252x-4860;
(2) From y = - 3x2 + 252x-4860, we know that y is a quadratic function of X,
The formula on the right side is y = - 3 (X-42) 2 + 432,
When x = 42, y has a maximum, y = 432,
When the selling price of each commodity is set at 42 yuan,
The maximum profit is 432 yuan per day
Representation is a basic problem

Mathematics problems of grade 9 (quadratic function part)
Known parabola C1: y = x ^ 2 + BX-1 passing through point (3,2)
(1) Find the analytic formula of the parabola C2 which is symmetric about the y-axis
(2) Find the analytic formula of the parabola C3 which is symmetric about X axis

Substituting the point (3,2) into the parabola, we get b = - 2
So the analytic formula of parabola C1 is y = x ^ 2-2x-1
The coordinates of the vertex are (1, - 2), and the coordinates of the y-axis symmetric point are (- 1, - 2),
So let the analytic expression of this parabola C2 symmetric about y axis be y = a (x + 1) ^ 2-2,
Because the opening direction and size are the same, so a = 1, so the analytical formula of parabola C2 is y = (x + 1) ^ 2-2, that is, y = x ^ 2 + 2x-1
In the same way, we can get the analytic expression of this parabola about X-axis symmetric parabola C3 as y = - x ^ 2 + 2x + 1

The height h (m) of the object emitted vertically meets the equation H = - 5T * t + vt. a park plans to design the maximum height of the fountain in the park to be 15m, so what is the speed of the fountain?

Set the spray speed as v0
V0=gt
Then t = V0 / g
h=-5(V0/g)^2+Vo^2/g=15
Then 5v0 ^ 2-v0 ^ 2G + 15g ^ 2 = 0
(5-g)V0^2+15g^2=0
Then V0 ^ 2 = 15g ^ 2 / (G-5)
V0=√[15/(g-5)]g