The minimum value of the quadratic function of one variable y = x2 ax + of X is 1 / 2

The minimum value of the quadratic function of one variable y = x2 ax + of X is 1 / 2

It's not easy to calculate the constant if you don't type it. Let me set the constant as C. y = (x-a / 2) (x-a / 2) + c-aa / 4. When x = A / 2, take the minimum value, that is, c-aa / 4 = 0.5, because C is known, so the value of a can be calculated

(1) The vertex coordinates of parabola y = 2x ^ 2 + 4x + 3 are? (2) the minimum value of quadratic function y = x ^ 2 + 4x + 6 is?

(1) The vertex is (- 1,1)
(2) The minimum value is y = 2

It is known that the quadratic trinomial x ^ 2-px-8 can decompose the factor in the range of rational number and find the possible value of integral P

（x+a)(x+b)
=x²+(a+b)x+ab
So p = - (a + b)
ab=-8=-8*1=-1*8=-2*4=-4*2
p=±7,±1

It is known that the quadratic trinomial x ^ 2-px-6 can decompose the factor in the range of rational number and find the possible value of integer P

By cross multiplication, - 6 can be regarded as the product of 1 and - 6 or the product of 2 and - 3 or - 1 and 6 or - 2 and 3, so p = - 5 or 1 or 5 or - 1

X ^ 4-7x ^ 2 + 6x factorization?

x^4-7x^2+6x
=x(x^3-7x+6)
=x[(x^3-1)-7x+7]
=x[(x-1)(x^2+x+1)-7(x-1)]
=x(x-1)(x^2+x+1-7)
=x(x-1)(x^2+x-6)
=x(x-1)(x+3)(x-2)

Factorization X & # 178; - 6x + 8 = 0

x²-6x+8=0
(x-2)(x-4)=0
x-2=0 x-4=0
x1=2 x2=4

Factorization x (6x-1) - 1

x（6x-1）-1
=6x^2-x-1
=(2x-1) (3x + 1) (cross multiplication)

Factorization: 9x ^ 2 - (X-Y) ^ 2

Factoring the square of X + 9x + 14

Original formula = x & # 178; + 2x + 7x + 14
=x(x+2)+7(x+2)
=(x+2)(x+7)

Factorization of x ^ 4-9x ^ 2

x^4-9x^2
=x²（x²-9)
=x²(x+3)(x-3)