Quadratics
Parabolas
Radicals
Misc
100
"What is the discriminant of "
2x^2+9=5x"?"
"The discriminant is "b^2-4ac
"The equation is "2x^2-5x+9=0
b^2-4ac=(-5)^2-4(2)(9)
=25-72=-47
100
"Name the vertex for "
y=-2(x-8)^2-5.
(8, -5)
100
sqrt(28a^2b)
Simplify. Assume variables are positive.
sqrt(28)sqrt(a^2)sqrt(b)
sqrt(4)sqrt(7)(a)sqrt(b)
2asqrt(7b)
100
"Solve "17=3+2sqrt(x)
14=2sqrt(x)" "implies" "7=sqrt(x)
(7)^2=(sqrt(x))^2
x=49
200
"Solve "10-7x+x^2=3(x-3)-2
10-7x+x^2=3x-9-2impliesx^2-10x+21=0
(x-7)(x-3)=0
x=7 or x=3
200
"What is the axis of symmetry for "
y=-2(x-8)^2-5.
"It is the vertical line that goes"
" through the vertex, so it is "x=8.
200
"Simplify "(sqrt(32)-3)(2+sqrt(8))
2sqrt(32)+sqrt(256)-6-3sqrt(8)" "implies" "2(4sqrt(2))+16-6-3(2sqrt(2))
8sqrt(2)+10-6sqrt(2)
10+2sqrt(2)
200
"Solve the system "{(3x,+,y,=,5),(x,-,4y,=,-7):}
3x+y=5" "implies" "y=5-3x " (substitute in 2nd equation)"
x-4(5-3x)=-7" "implies" "x-20+12x=-7" "implies" "x=1
y=5-3x" "implies" "y=5-3(1)" "implies" "y=2
"solution: "(1,2)
300
"Solve "x^2+5x-1=0.
x=(-bpmsqrt(b^2-4ac))/(2a)
x=(-5pmsqrt(25-4(1)(-1)))/(2(1))
x=(-5pmsqrt(29))/(2)
300
"Graph "y=(x-2)^2-3
300
"Simplify "(sqrt(12)-3sqrt(2))/sqrt(3)
((sqrt(12)-3sqrt(2)))/sqrt(3)cdot((sqrt(3)))/((sqrt(3)))=(sqrt(36)-3sqrt(6))/3=(6-3sqrt(6))/3
=6/3-(3sqrt(6))/3=2-sqrt(6)
400
"Find the zeros of "
f(x)=x^2-4x-12.
0=(x-6)(x+2)
"The zeros are 6 and -2."
500
"Complete the square for "
f(x)=x^2-4x-12 " and put in graphing form."
f(x)=(x^2-4x+"___")-12-"___ "
f(x)=(x^2-4x+4)-12-4
f(x)=(x-2)^2-16