Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
42001	Find the Vertex	(x+3)^2=-8(y-2)	${(x + 3)}^{2} = - 8 (y - 2)$
42002	Find the Vertex	x^2-14x+4y+29=0	$x^{2} - 14 x + 4 y + 29 = 0$
42003	Find the Vertex	x^2-16y=0	$x^{2} - 16 y = 0$
42004	Find the Vertex	y^2=28x	$y^{2} = 28 x$
42005	Find the Vertex	y^2=-20x	$y^{2} = - 20 x$
42006	Find the Vertex	y^2=24x	$y^{2} = 24 x$
42007	Find the Vertex	y^2=-14x	$y^{2} = - 14 x$
42008	Find the Vertex	y^2+2x-8y+4=0	$y^{2} + 2 x - 8 y + 4 = 0$
42009	Find the Vertex	y^2+4y-x=0	$y^{2} + 4 y - x = 0$
42010	Find the Vertex	y^2+6y+8x+1=0	$y^{2} + 6 y + 8 x + 1 = 0$
42011	Find the Vertex	x^2=60y	$x^{2} = 60 y$
42012	Find the Vertex	y=3x^2+2x+1	$y = 3 x^{2} + 2 x + 1$
42013	Find Trig Functions Using Identities	sin(theta)(cot(theta)+tan(theta))=sec(theta)	$\sin (θ (\cot (θ) + \tan (θ))) = \sec (θ)$
42014	Determine if Odd, Even, or Neither	f(x)=7x^(3/4)	$f (x) = 7 x^{\frac{3}{4}}$
42015	Determine if Odd, Even, or Neither	f(x)=-7x^2+1	$f (x) = - 7 x^{2} + 1$
42016	Find the Roots (Zeros)	f(x)=x^3+2x^2-5x-10	$f (x) = x^{3} + 2 x^{2} - 5 x - 10$
42017	Find the Roots (Zeros)	f(x)=x^3-3x^2-10x	$f (x) = x^{3} - 3 x^{2} - 10 x$
42018	Find the Roots (Zeros)	f(x)=x^3-5x^2-2x+24	$f (x) = x^{3} - 5 x^{2} - 2 x + 24$
42019	Find the Roots (Zeros)	f(x)=x^3-7x^2+17x-15	$f (x) = x^{3} - 7 x^{2} + 17 x - 15$
42020	Find the Roots (Zeros)	P(x)=4x^4+8x^3-7x^2-21x-9	$P (x) = 4 x^{4} + 8 x^{3} - 7 x^{2} - 21 x - 9$
42021	Find the Roots (Zeros)	h(x)=6x^3-41x^2-8x+7	$h (x) = 6 x^{3} - 41 x^{2} - 8 x + 7$
42022	Find the Roots (Zeros)	P(x)=x^4-13x^2+36	$P (x) = x^{4} - 13 x^{2} + 36$
42023	Find the Roots (Zeros)	f(x)=x^4+122x^2+121	$f (x) = x^{4} + 122 x^{2} + 121$
42024	Find the Roots (Zeros)	f(x)=\|x^2-25\|	$f (x) = \| x^{2} - 25 \|$
42025	Find the Roots (Zeros)	f(x)=3x^3-5x^2-12x+20	$f (x) = 3 x^{3} - 5 x^{2} - 12 x + 20$
42026	Find the Roots (Zeros)	f(x)=6x^3-43x^2+6x+7	$f (x) = 6 x^{3} - 43 x^{2} + 6 x + 7$
42027	Find the Roots (Zeros)	F(x)=x^2+6x+8	$F (x) = x^{2} + 6 x + 8$
42028	Find the Roots (Zeros)	f(x)=x^2e^x-25e^x	$f (x) = x^{2} e^{x} - 25 e^{x}$
42029	Find the Roots (Zeros)	f(x)=x^3+13x^2+47x+35	$f (x) = x^{3} + 13 x^{2} + 47 x + 35$
42030	Find the Slope of a Perpendicular Line	y=2x+5	$y = 2 x + 5$
42031	Find the Domain and Range	e^x-2	$e^{x} - 2$
42032	Find the Domain and Range	10-x^2	$10 - x^{2}$
42033	Evaluate the Function	f(3)=4^x	$f (3) = 4^{x}$
42034	Find the Variables	[[2],[9],[0]]=[[x],[y],[0]]	$[\begin{array}{c} 2 \\ 9 \\ 0 \end{array}] = [\begin{array}{c} x \\ y \\ 0 \end{array}]$
42035	Find the Trig Value	cos(theta)=3/4	$\cos (θ) = \frac{3}{4}$
42036	Expand Using Pascal's Triangle	(x+y)^2	${(x + y)}^{2}$
42037	Find the Determinant	[[-2,2,1],[9,1,-2],[-3,5,4]]	$[\begin{array}{c} - 2 & 2 & 1 \\ 9 & 1 & - 2 \\ - 3 & 5 & 4 \end{array}]$
42038	Find the Center	9x^2-54x+9y^2-54y+81=0	$9 x^{2} - 54 x + 9 y^{2} - 54 y + 81 = 0$
42039	Write as a Single Logarithm	3 log base 4 of x^2+1/2 log base 4 of square root of x	$3 \log_{4} (x^{2}) + \frac{1}{2} \log_{4} (\sqrt{x})$
42040	Identify the Sequence	20 , 18.5 , 17 , 15.5 , 14	$20$ , $18.5$ , $17$ , $15.5$ , $14$
42041	Identify the Sequence	25 , -175 , -375 , -575	$25$ , $- 175$ , $- 375$ , $- 575$
42042	Identify the Sequence	1 , 1/2 , 1/6 , 1/24 , 1/120	$1$ , $\frac{1}{2}$ , $\frac{1}{6}$ , $\frac{1}{24}$ , $\frac{1}{120}$
42043	Write in Standard Form	2-2 square root of 3i	$2 - 2 \sqrt{3 i}$
42044	Find the x and y Intercepts	3x^2+18x+3y^2=0	$3 x^{2} + 18 x + 3 y^{2} = 0$
42045	Find the x and y Intercepts	theta=(2pi)/3	$θ = \frac{2 π}{3}$
42046	Find the x and y Intercepts	t=pi/4	$t = \frac{π}{4}$
42047	Find the x and y Intercepts	x=3y^2+30y+69	$x = 3 y^{2} + 30 y + 69$
42048	Find the x and y Intercepts	y^2=1296-36x^2	$y^{2} = 1296 - 36 x^{2}$
42049	Find the x and y Intercepts	y^2=4096-64x^2	$y^{2} = 4096 - 64 x^{2}$
42050	Find the Derivative - d/d@VAR	f(x)=(x^(2/3)-1)^2	$f (x) = {(x^{\frac{2}{3}} - 1)}^{2}$
42051	Find the Derivative - d/d@VAR	f(x)=4x^4-5x-3	$f (x) = 4 x^{4} - 5 x - 3$
42052	Find the Derivative - d/d@VAR	h(t)=12t^2-6t+50	$h (t) = 12 t^{2} - 6 t + 50$
42053	Find the Asymptotes	(2x^3+11x^2+5x-1)/(x^2+6x+5)	$\frac{2 x^{3} + 11 x^{2} + 5 x - 1}{x^{2} + 6 x + 5}$
42054	Find the Asymptotes	(2x^2+1)/x	$\frac{2 x^{2} + 1}{x}$
42055	Find the Asymptotes	(x^2-x+8)/(x-3)	$\frac{x^{2} - x + 8}{x - 3}$
42056	Find the Vertex Form	y=-3x^2+48x-199	$y = - 3 x^{2} + 48 x - 199$
42057	Find the Vertex Form	y=x^2-10x+25	$y = x^{2} - 10 x + 25$
42058	Convert to Logarithmic Form	6^(2x)+6^x-12=0	$6^{2 x} + 6^{x} - 12 = 0$
42059	Convert to Logarithmic Form	10^0.9542=9	$10^{0.9542} = 9$
42060	Find the Difference Quotient	f(x)=6x	$f (x) = 6 x$
42061	Find the Degree	theta=(11pi)/6	$θ = \frac{11 π}{6}$
42062	Write in Standard Form	y^2+6y+9=12-12x	$y^{2} + 6 y + 9 = 12 - 12 x$
42063	Write in Standard Form	y^2-4y+4x+4=0	$y^{2} - 4 y + 4 x + 4 = 0$
42064	Write in Standard Form	y^2-12y-x^2-2x+31=0	$y^{2} - 12 y - x^{2} - 2 x + 31 = 0$
42065	Write in Standard Form	x^2-8x+5y+31=0	$x^{2} - 8 x + 5 y + 31 = 0$
42066	Write in Standard Form	x^2-y^2-2x-10y-25=0	$x^{2} - y^{2} - 2 x - 10 y - 25 = 0$
42067	Write in Standard Form	x^2-y^2-4x-6y-6=0	$x^{2} - y^{2} - 4 x - 6 y - 6 = 0$
42068	Write in Standard Form	9x^2+16y^2=144	$9 x^{2} + 16 y^{2} = 144$
42069	Write in Standard Form	6x^2+2y^2+18x-10y+2=0	$6 x^{2} + 2 y^{2} + 18 x - 10 y + 2 = 0$
42070	Write in Standard Form	4x^2-y^2=16	$4 x^{2} - y^{2} = 16$
42071	Write in Standard Form	9x^2+4y^2-72x+40y+208=0	$9 x^{2} + 4 y^{2} - 72 x + 40 y + 208 = 0$
42072	Write in Standard Form	9x^2+4y^2-54x+16y+61=0	$9 x^{2} + 4 y^{2} - 54 x + 16 y + 61 = 0$
42073	Write in Standard Form	-9x^2+4y^2-36x-16y-164=0	$- 9 x^{2} + 4 y^{2} - 36 x - 16 y - 164 = 0$
42074	Write in Standard Form	16y^2-x^2+2x+64y+63=0	$16 y^{2} - x^{2} + 2 x + 64 y + 63 = 0$
42075	Write in Standard Form	16x^2+4y^2+256x-16y+976=0	$16 x^{2} + 4 y^{2} + 256 x - 16 y + 976 = 0$
42076	Write in Standard Form	-16x^2+4y^2-256x-48y-944=0	$- 16 x^{2} + 4 y^{2} - 256 x - 48 y - 944 = 0$
42077	Write in Standard Form	16x^2-9y^2-192x-36y+396=0	$16 x^{2} - 9 y^{2} - 192 x - 36 y + 396 = 0$
42078	Write in Standard Form	25x^2+9y^2-50x-90y+25=0	$25 x^{2} + 9 y^{2} - 50 x - 90 y + 25 = 0$
42079	Write in Standard Form	36x^2+100y^2-144x+400y-3056=0	$36 x^{2} + 100 y^{2} - 144 x + 400 y - 3056 = 0$
42080	Write in Standard Form	36x^2+100y^2-216x+200y-3176=0	$36 x^{2} + 100 y^{2} - 216 x + 200 y - 3176 = 0$
42081	Write in Standard Form	4x^2-16y^2-16x-128y-304=0	$4 x^{2} - 16 y^{2} - 16 x - 128 y - 304 = 0$
42082	Write in Standard Form	4x^2+y^2-32x+16y+124=0	$4 x^{2} + y^{2} - 32 x + 16 y + 124 = 0$
42083	Write in Standard Form	4x^2-9y^2-8x+40=0	$4 x^{2} - 9 y^{2} - 8 x + 40 = 0$
42084	Write in Standard Form	4x^2+25y^2-8x+150y+129=0	$4 x^{2} + 25 y^{2} - 8 x + 150 y + 129 = 0$
42085	Write in Standard Form	4x^2+8x+5y^2-30y-11=0	$4 x^{2} + 8 x + 5 y^{2} - 30 y - 11 = 0$
42086	Find the Slope of a Perpendicular Line	y=x+4	$y = x + 4$
42087	Expand the Trigonometric Expression	tan(2theta)	$\tan (2 θ)$
42088	Expand the Trigonometric Expression	cos(5theta)+cos(3theta)	$\cos (5 θ) + \cos (3 θ)$
42089	Expand the Trigonometric Expression	cos(90 degrees -x)	$\cos (90 ° - x)$
42090	Find the Domain	f(x)=(x-5)/( square root of x+6)	$f (x) = \frac{x - 5}{\sqrt{x + 6}}$
42091	Find the Domain	f(x)=(2x+1)/(x-4)	$f (x) = \frac{2 x + 1}{x - 4}$
42092	Find the Domain	f(x) = log base 5 of 11-x	$f (x) = \log_{5} (11 - x)$
42093	Find the Standard Form of the Parabola	y^2+4x-16y+72=0	$y^{2} + 4 x - 16 y + 72 = 0$
42094	Find the Standard Form of the Parabola	y^2-2x-2y-9=0	$y^{2} - 2 x - 2 y - 9 = 0$
42095	Find the Standard Form of the Parabola	x^2+10x-2y+11=0	$x^{2} + 10 x - 2 y + 11 = 0$
42096	Find the Standard Form of the Parabola	x^2+2x-2y-5=0	$x^{2} + 2 x - 2 y - 5 = 0$
42097	Find the Asymptotes	f(x)=e^(x-6)	$f (x) = e^{x - 6}$
42098	Find the Asymptotes	f(x)=6e^(-x)	$f (x) = 6 e^{- x}$
42099	Find the Asymptotes	g(x)=2^(x-3)	$g (x) = 2^{x - 3}$
42100	Find the Asymptotes	s(x)=(6x^2+1)/(2x^2+9x-5)	$s (x) = \frac{6 x^{2} + 1}{2 x^{2} + 9 x - 5}$