`a)A=-2x²+5x-15`
`=-2(x²-5/2x+15/2)`
`=-2(x²-5/2x+25/16+95/16)`
`=-2(x²-5/2x+25/16)-95/8`
`=-2[x²-2.x. 5/4+(5/4)^2]-95/8`
`=-2(x-5/4)^2-95/8`
Ta có:`(x-5/4)^2≥0∀x`
`⇒2(x-5/4)^2≥0∀x`
`⇒-2(x-5/4)^2≤0∀x`
`⇒-2(x-5/4)^2-95/8≤-95/8∀x`
Vậy `A_(max)=-95/8` khi `x-5/4=0⇔=5/4`
`c)C=-4x²-4x-7`
`=-4(x²+x+7/4)`
`=-4(x²+x+1/4+3/2)`
`=-4(x²+x+1/4)-6`
`=-4[x²+2.x. 1/2+(1/2)^2]-6`
`=-4(x+1/2)^2-6`
Ta có:`(x+1/2)^2≥0∀x`
`⇒4(x+1/2)^2≥0∀x`
`⇒-4(x+1/2)^2≤0∀x`
`⇒-4(x+1/2)^2-6≤-6∀x`
Vậy `C_(max)=-6` khi `x+1/2=0⇔x=-1/2`
`d)D=-10-8x-16x²`
`=-(16x²+8x+10)`
`=-(16x²+8x+1+9)`
`=-(16x²+8x+1)-9`
`=-[(4x)²+2.4x.1+1²]-9`
`=-(4x+1)²-9`
Ta có:`(4x-1)²≥0∀x`
`⇒-(4x-1)²≤0∀x`
`⇒-(4x-1)²-9≤-9∀x`
Vậy `D_(max)=-9` khi `4x-1=0⇔x=1/4`
`e)E=-3x²+12x-13`
`=-3(x²-4x+13/3)`
`=-3(x²-4x+4+1/3)`
`=-3(x²-4x+4)-1`
`=-3(x²-2.x.2+2²)-1`
`=-3(x-2)²-1`
Ta có:`(x-2)²≥0∀x`
`⇒3(x-2)²≥0∀x`
`⇒-3(x-2)²≤0∀x`
`⇒-3(x-2)²-1≤-1`
Ta có:`(x-2)²≥0∀x`
`⇒3(x-2)²≥0∀x`
`⇒-3(x-2)²≤0∀x`
`⇒-3(x-2)²-1≤-1∀x`
Vậy `E_(max)=-1` khi `x-2=0⇔x=2`
