image imagewidth (px) 2 3.75k | material_type stringclasses 2
values | latex listlengths 1 1 |
|---|---|---|
HW | [
"$\\displaystyle -14$"
] | |
HW | [
"$\\displaystyle \\alpha\\beta = -2-b=-2, b=0.$"
] | |
HW | [
"$\\displaystyle \\alpha\\beta = -2-b=-2, b=0.$"
] | |
HW | [
"$\\displaystyle b-a =0 -3 = -3$"
] | |
HW | [
"$\\displaystyle m=-\\left(a^{2}+32 a+16^{2}\\right)-16^{2}+2$"
] | |
HW | [
"$\\displaystyle y=(x-3)(x+3)$"
] | |
HW | [
"$\\displaystyle 0$"
] | |
HW | [
"$\\displaystyle y=\\left(x^{2}-2 a x+a^{2}\\right)-a^{2}+12 a+1$"
] | |
HW | [
"$\\displaystyle y=\\left(x^{2}-2 a x+a^{2}\\right)-a^{2}+12 a+1$"
] | |
HW | [
"$\\displaystyle y=(k-a)^{2}-a^{2}+12 a+1$"
] | |
HW | [
"$\\displaystyle y=(k-a)^{2}-a^{2}+12 a+1$"
] | |
HW | [
"$\\displaystyle m=-a^{2}+12 a+1$"
] | |
HW | [
"$\\displaystyle m=-a^{2}+12 a+1$"
] | |
HW | [
"$\\displaystyle m=-\\left(a^{2}-16 a+6 4\\right)+65$"
] | |
HW | [
"$\\displaystyle m=-\\left(a^{2}-16 a+6 4\\right)+65$"
] | |
HW | [
"65"
] | |
HW | [
"65"
] | |
HW | [
"good!"
] | |
HW | [
"$\\displaystyle y=\\left(x^{2}+2 a x+a^{2}\\right)-a^{2}+b$"
] | |
HW | [
"$\\displaystyle y=\\left(x^{2}+2 a x+a^{2}\\right)-a^{2}+b$"
] | |
HW | [
"$\\displaystyle y=(x+6)^{2}-36+b \\quad b=36$"
] | |
HW | [
"$\\displaystyle y=(x+6)^{2}-36+b \\quad b=36$"
] | |
HW | [
"$\\displaystyle y=-2\\left(A^{2}-2 A+1\\right)+4 A+k+3$"
] | |
HW | [
"$\\displaystyle y=-2\\left(A^{2}-2 A+1\\right)+4 A+k+3$"
] | |
HW | [
"$\\displaystyle y=-2 A^{2}+4 A-2+4 A+k+3$"
] | |
HW | [
"$\\displaystyle y=-2 A^{2}+4 A-2+4 A+k+3$"
] | |
HW | [
"$\\displaystyle y=-2 A^{2}+8 A+k+1$"
] | |
HW | [
"$\\displaystyle y=-2 A^{2}+8 A+k+1$"
] | |
HW | [
"$\\displaystyle y=-2\\left(A^{2}-4 A+4\\right)+k+9$"
] | |
HW | [
"$\\displaystyle y=-2\\left(A^{2}-4 A+4\\right)+k+9$"
] | |
HW | [
"$\\displaystyle k+9=4$"
] | |
HW | [
"$\\displaystyle k+9=4$"
] | |
HW | [
"$\\displaystyle 26$"
] | |
HW | [
"$\\displaystyle 26$"
] | |
HW | [
"$\\displaystyle k=-1$"
] | |
HW | [
"$\\displaystyle k=-1$"
] | |
HW | [
"$\\displaystyle x^{2}+4x=A \\quad A=(x+2)^{2}-2$"
] | |
HW | [
"$\\displaystyle x^{2}+4x=A \\quad A=(x+2)^{2}-2$"
] | |
HW | [
"$\\displaystyle y=A^{2}+6 A+1$"
] | |
HW | [
"$\\displaystyle y=(A+3)^{2}-q$"
] | |
HW | [
"$\\displaystyle y=(A+3)^{2}-q$"
] | |
HW | [
"$\\displaystyle D=9+(24 \\times 9_{k})=9+216 k$"
] | |
HW | [
"$\\displaystyle D=9+(24 \\times 9_{k})=9+216 k$"
] | |
HW | [
"$\\displaystyle \\therefore k=-\\frac{9}{216}$"
] | |
HW | [
"$\\displaystyle -\\frac{9}{216}$"
] | |
HW | [
"$\\displaystyle =-\\frac{1}{24}$"
] | |
HW | [
"$\\displaystyle y = (x+7)^{2} + 4$"
] | |
HW | [
"$\\displaystyle y = (x+7)^{2} + 4$"
] | |
HW | [
"$\\displaystyle d=2^{2}+14 x+53$"
] | |
HW | [
"$\\displaystyle d=2^{2}+14 x+53$"
] | |
HW | [
"$\\displaystyle \\therefore 2 a=14, \\quad a=7$"
] | |
HW | [
"$\\displaystyle \\therefore 2 a=14, \\quad a=7$"
] | |
HW | [
"60"
] | |
HW | [
"60"
] | |
HW | [
"$\\displaystyle a+b=60$"
] | |
HW | [
"$\\displaystyle a+b=60$"
] | |
HW | [
"$\\displaystyle y=-2\\left(x^{2}-6 x+1\\right)^{2}+4\\left(x^{2}-6 x\\right)+k-4$"
] | |
HW | [
"$\\displaystyle x^{2}-6 x+1=t\\quad y=-2t^{2}+4(t-1)+k-4$"
] | |
HW | [
"$\\displaystyle x^{2}-6 x+1=t\\quad y=-2t^{2}+4(t-1)+k-4$"
] | |
HW | [
"$\\displaystyle =-2 t^{2}+4 t+k-8$"
] | |
HW | [
"$\\displaystyle =-2 t^{2}+4 t+k-8$"
] | |
HW | [
"$\\displaystyle =-2\\left(t^{2}-2 t+1\\right)+k-6$"
] | |
HW | [
"$\\displaystyle k-6=3 \\quad \\therefore \\quad k=9$"
] | |
HW | [
"$\\displaystyle a+b=43$"
] | |
HW | [
"$\\displaystyle a+b=43$"
] | |
HW | [
"$\\displaystyle D>0, \\quad D=9+24 k$"
] | |
HW | [
"$\\displaystyle 9+24 k>0, \\quad 24 k>-9, \\quad k>\\frac{-9}{24}$"
] | |
HW | [
"$\\displaystyle k > \\frac{-3}{8}$"
] | |
HW | [
"$\\displaystyle >0$"
] | |
HW | [
"$\\displaystyle >0$"
] | |
HW | [
"$\\displaystyle (a+k)^{2}-k^{2}-4 k-b=0$"
] | |
HW | [
"$\\displaystyle (a+k)^{2}-k^{2}-4 k-b=0$"
] | |
HW | [
"$\\displaystyle k^{2}+2 a k+a^{2}-k^{2}-4 k-b=0$"
] | |
HW | [
"$\\displaystyle k^{2}+2 a k+a^{2}-k^{2}-4 k-b=0$"
] | |
HW | [
"$\\displaystyle a=2, b=4, a b=8$."
] | |
HW | [
"$\\displaystyle a=2, b=4, a b=8$."
] | |
HW | [
"$\\displaystyle 2\\left(x^{2}-6 x\\right)+y^{2}+4 y+14$"
] | |
HW | [
"ok?"
] | |
HW | [
"$\\displaystyle \\therefore -8$"
] | |
HW | [
"$\\displaystyle -8$"
] | |
HW | [
"$\\displaystyle y=11^{2}+(10-m) x+\\frac{m^{2}}{4}$"
] | |
HW | [
"$\\displaystyle (10-m)^{2}-4(\\frac{m^{2}}{4})>0$"
] | |
HW | [
"$\\displaystyle (10-m)^{2}-4(\\frac{m^{2}}{4})>0$"
] | |
HW | [
"$\\displaystyle 100-20 m+m^{2}-m^{2}>0$"
] | |
HW | [
"$\\displaystyle 100-20 m+m^{2}-m^{2}>0$"
] | |
HW | [
"$\\displaystyle y=2 x+6$"
] | |
HW | [
"$\\displaystyle -3 x^{2}+x-3=2 x+6$"
] | |
HW | [
"$\\displaystyle -3 x^{2}+x-3=2 x+6$"
] | |
HW | [
"$\\displaystyle -3 x^{2}+x-2 x-3-6=0$"
] | |
HW | [
"$\\displaystyle -3 x^{2}-x-9=0$"
] | |
HW | [
"$\\displaystyle -3 x^{2}-x-9=0$"
] | |
HW | [
"$\\displaystyle 3 x^{2}+x+9=0$"
] | |
HW | [
"$\\displaystyle 3 x^{2}+x+9=0$"
] | |
HW | [
"$\\displaystyle D=1-4(27)$"
] | |
HW | [
"$\\displaystyle D=1-4(27)$"
] | |
HW | [
"$\\displaystyle \\therefore D<0$"
] | |
HW | [
"$\\displaystyle \\therefore D<0$"
] | |
HW | [
"$\\displaystyle y=75\\left(x^{2}+2 x+1\\right)$"
] | |
HW | [
"$\\displaystyle y=75\\left(x^{2}+2 x+1\\right)$"
] | |
HW | [
"$\\displaystyle y=75(x+1)^{2}$"
] |
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