What is the sum and product formula of two quadratic equations of one variable? Is the sum and product formula of X1 and x2

What is the sum and product formula of two quadratic equations of one variable? Is the sum and product formula of X1 and x2

a(x-x1)(x-x2)=0
axx-a(x1+x2)x+ax1x2=0
axx+bx+c=0
-a(x1+x2)=b
ax1x2=c
x1+x2=-b/a
x1x2=c/a

What is the sum of two and the product of two in a quadratic equation of one variable?

Ax ^ 2 + BX + C = 0
x1+x2=-b/a
x1x2=c/a

What is the sum of two quadratic equations of one variable? What's the difference?

Univariate quadratic equation AX ^ 2 + BX + C = 0 (a \ B \ C is the coefficient)
Let two be p and Q
According to the root relationship, the sum is p + q = - B / A
The product of is PQ = C / A
(p-q)^2=(p+q)^2-4pq= (-b/a)^2-c/a=(b^2-c^2)/a^2
So the difference P-Q = under the quadratic root ((b ^ 2-C ^ 2) / A ^ 2)

When x is equal to - 1, the function value is 10, when x is equal to 1, the function value is 4, and when x is equal to 2, the function value is 7. Find the analytical formula of the quadratic function (coefficient to be determined)

Let the analytic expression of this quadratic function be y = ax ²+ BX + C (a is not equal to 0) will x = - 1, y = 10; x=1,y=4； X = 2 and y = 7 are respectively substituted into the analytical formula to get (- 1) (- 1) a + (- 1) B + C = A-B + C = 10 (1) 1 * 1 * a + 1 * B + C = a + B + C = 4 (2) 2 * 2 * a + 2 * B + C = 4A + 2B + C = 7 (3) simultaneous (1) (2) (3) to get three yuan one

Who will help me compile a quadratic function with a quadratic term coefficient of 1, so that when x = 4, the function value is 16, then the compiled function is?

y=x^2
y=x^2-4x+16
. etc

Judge whether the following function is a quadratic function. If it is a quadratic function, please state its quadratic term coefficient, primary term coefficient and constant term （1）y=2x ²- 3； （2）y=3x-1； （3）y=（2x-1）（1-x）； （4）y=1/x ²+ one

（1）y=2x ²- The coefficient of quadratic term of quadratic function is 2
The coefficient of the first-order term is 0 and the constant term is - 3
(2) Y = 3x-1 is not a quadratic function
(3) Y = (2x-1) (1-x) is a quadratic function, the coefficient of the quadratic term is - 2, the coefficient of the primary term is 3, and the constant term is - 1
（4）y=1/x ²+ 1 is not a quadratic function