LÀM XONG NHỚ T.I.C.K Á

F(0)=3 =>C=3

F(1)=0=>A+B+C=0=>A+B= -3   (1)

F(-1)=1=>A+B+C=1=>A-B= -2   (2)

KẾT HỢP 1 VÀ 2 =>A=5/2;B=1/2

\(f\left(0\right)=5=>c=5;f\left(2\right)=4.a+2.b+5=0;f\left(5\right)=25a+5b+5=0\Leftrightarrow5a+b+1=0\)

\(\hept{\begin{cases}4a+2b+5=0\\5a+b+1=0\end{cases}}\)\(\Leftrightarrow\hept{\begin{cases}4a+2b+5=0\\10a+2b+2=0\end{cases}}\)\(\Leftrightarrow\hept{\begin{cases}4a+2b+5=0\\6a-3=0\end{cases}}\)\(\Leftrightarrow\hept{\begin{cases}b=-\frac{7}{2}\\a=\frac{1}{2}\end{cases}}\)

\(f\left(x\right)=\frac{1}{2}x^2-\frac{7}{2}x+5\)

b)

\(f\left(-1\right)=\frac{1}{2}+\frac{7}{2}+5=9=>P\left(-1;3\right)kothuocHS\)

\(f\left(\frac{1}{2}\right)=\frac{1}{2}.\frac{1}{4}-\frac{7}{2}.\frac{1}{2}+5=\frac{\left(1-14+5.8\right)}{8}=\frac{27}{8}=>Qkothuoc\)

c)

\(\frac{1}{2}x^2-\frac{7}{2}x+5=-3\Rightarrow\frac{1}{2}x^2-\frac{7}{2}x+8=0\)

\(x^2-7x+16=0\Leftrightarrow\left(x^2-2.\frac{7}{2}x+\frac{49}{4}\right)+\frac{15}{4}\)vo nghiem

f(0)=3  =>c=3

f(1)=0 => a+b+c=0 =>a+b=-3     (1)

f(-1)=1 => a-b+c=1 =>a-b=-2      (2)

Kết hợp (1) và (2) => a=-5/2 ; b=-1/2

Theo de ta co:

f(0) = a.0²+b.0+c = c =1

f(1)=a.1²+b.1+c = a+b+1 = 2  => a+b = 1

f(2)=a.2²+b.2+c = 4a+2b+1=2(2a+b)+1 = 4  => 2(2a+b) = 3  => 2a+b = 3/2 => b = 3/2 - 2a

Thay b=3/2 - 2a vao bieu thuc: a+b=1  ta duoc:

a+3/2-2a = 1

3/2-a= 1

=> a = 3/2 - 1 = 1/2

Suy ra: b = 3/2 - 2.1/2  = 1/2

Vay: a = 1/2   ;    b=1/2       ;      c=1

Neu f(0)=3=>a=1;b=2 va c=3

Neu f(1)=0=>a=0;b=0 ca c=0

Neu f(-1)=1=>a=-1;b=-1 va c=-1