Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
5101	Find the Upper and Lower Bounds	f(x)=x^4+4x^3-2x-3	$f (x) = x^{4} + 4 x^{3} - 2 x - 3$
5102	Find the Upper and Lower Bounds	f(x)=x^4+x^3-11x^2-9x+18	$f (x) = x^{4} + x^{3} - 11 x^{2} - 9 x + 18$
5103	Find the Upper and Lower Bounds	f(x)=x^4-3x^3-2x^2+3x-5	$f (x) = x^{4} - 3 x^{3} - 2 x^{2} + 3 x - 5$
5104	Find the Upper and Lower Bounds	f(x)=x^4-4x^3+16x-16	$f (x) = x^{4} - 4 x^{3} + 16 x - 16$
5105	Find the Maximum Number of Real Roots	P(x)=x^3-x-6	$P (x) = x^{3} - x - 6$
5106	Find the Maximum Number of Real Roots	y=x^2+2x+1	$y = x^{2} + 2 x + 1$
5107	Find the Maximum Number of Real Roots	y=2sin(4x-pi)	$y = 2 \sin (4 x - π)$
5108	Find the Maximum Number of Real Roots	p(x)=3x^4-11x^3-3x^2-6x+8	$p (x) = 3 x^{4} - 11 x^{3} - 3 x^{2} - 6 x + 8$
5109	Find the Maximum Number of Real Roots	-9i	$- 9 i$
5110	Find the Maximum Number of Real Roots	f(x)=-2x-x^7	$f (x) = - 2 x - x^{7}$
5111	Find the Maximum Number of Real Roots	h(t)=40t-16t^2	$h (t) = 40 t - 16 t^{2}$
5112	Find the Maximum Number of Real Roots	f(x)=a(x-6)(x-i)(x+i)(x+(9+i))(x+(9-i))	$f (x) = a (x - 6) (x - i) (x + i) (x + (9 + i)) (x + (9 - i))$
5113	Find the Maximum Number of Real Roots	f(x)=2x^5-5x^2+x-4	$f (x) = 2 x^{5} - 5 x^{2} + x - 4$
5114	Find the x and y Intercepts	f(x)=3x^3-5x+7	$f (x) = 3 x^{3} - 5 x + 7$
5115	Find the x and y Intercepts	f(x)=3x^3-7x^2-75x+175	$f (x) = 3 x^{3} - 7 x^{2} - 75 x + 175$
5116	Find the Maximum Number of Real Roots	f(x)=x^5+7x^4+2x^3+14x^2+x+7	$f (x) = x^{5} + 7 x^{4} + 2 x^{3} + 14 x^{2} + x + 7$
5117	Find the Maximum Number of Real Roots	f(x)=x^3-5x^2-9x+45	$f (x) = x^{3} - 5 x^{2} - 9 x + 45$
5118	Find the Maximum Number of Real Roots	f(x)=x^4+41x^2+400	$f (x) = x^{4} + 41 x^{2} + 400$
5119	Find the Maximum Number of Real Roots	f(x)=11x^3+12x^2+12x+1	$f (x) = 11 x^{3} + 12 x^{2} + 12 x + 1$
5120	Find the Vertex	h(x)=2x^2-x+1	$h (x) = 2 x^{2} - x + 1$
5121	Find the Vertex	w(x)=6-2x-4x^2	$w (x) = 6 - 2 x - 4 x^{2}$
5122	Find the Maximum/Minimum Value	(x+3)(x-2)=0	$(x + 3) (x - 2) = 0$
5123	Find the Maximum/Minimum Value	(3x)^2-2x-5	${(3 x)}^{2} - 2 x - 5$
5124	Find the Maximum/Minimum Value	2/3n-1/90n^2	$\frac{2}{3} n - \frac{1}{90} n^{2}$
5125	Find the Maximum/Minimum Value	2x^2-8x+3	$2 x^{2} - 8 x + 3$
5126	Find the Maximum/Minimum Value	3x^2-6x+13	$3 x^{2} - 6 x + 13$
5127	Find the Maximum/Minimum Value	-4x^2-16x+3	$- 4 x^{2} - 16 x + 3$
5128	Find the Maximum/Minimum Value	92t-16t^2	$92 t - 16 t^{2}$
5129	Find the Maximum/Minimum Value	f(x)=-4/9x^2+24/9x+12	$f (x) = - \frac{4}{9} x^{2} + \frac{24}{9} x + 12$
5130	Find the Maximum/Minimum Value	f(x)=-1/2x^2-2x+6	$f (x) = - \frac{1}{2} x^{2} - 2 x + 6$
5131	Find the Maximum/Minimum Value	F(x)=3x^2+12x-7	$F (x) = 3 x^{2} + 12 x - 7$
5132	Find the Maximum/Minimum Value	f(x)=-1/7x^2+100x	$f (x) = - \frac{1}{7} x^{2} + 100 x$
5133	Find the Maximum/Minimum Value	f(x)=-(x-5)^2+5	$f (x) = - {(x - 5)}^{2} + 5$
5134	Find the Maximum/Minimum Value	-2x^2+12x-3	$- 2 x^{2} + 12 x - 3$
5135	Find the Maximum/Minimum Value	f(x)=4x^2-16x+1000	$f (x) = 4 x^{2} - 16 x + 1000$
5136	Find the Maximum/Minimum Value	x^2+2x-1	$x^{2} + 2 x - 1$
5137	Find the Maximum/Minimum Value	f(t)=100-49t-7t^2	$f (t) = 100 - 49 t - 7 t^{2}$
5138	Find the Maximum/Minimum Value	f(x)=-2x^2+5x-2	$f (x) = - 2 x^{2} + 5 x - 2$
5139	Find the Maximum/Minimum Value	f(x)=x^2+2x-6	$f (x) = x^{2} + 2 x - 6$
5140	Find the Maximum/Minimum Value	f(x)=x^2+2x-4	$f (x) = x^{2} + 2 x - 4$
5141	Find the Maximum/Minimum Value	f(x)=x^2+10x+28	$f (x) = x^{2} + 10 x + 28$
5142	Find the Maximum/Minimum Value	f(x)=-1/2x^2-2x+2	$f (x) = - \frac{1}{2} x^{2} - 2 x + 2$
5143	Find the Maximum/Minimum Value	f(x)=-32/((20)^2)x^2+x+5	$f (x) = - \frac{32}{{(20)}^{2}} x^{2} + x + 5$
5144	Find the Maximum/Minimum Value	f(x)=x^2+9x-16	$f (x) = x^{2} + 9 x - 16$
5145	Find the Maximum/Minimum Value	f(x)=-x^2+6x-10	$f (x) = - x^{2} + 6 x - 10$
5146	Find the Maximum/Minimum Value	f(x)=x^2+4x-8	$f (x) = x^{2} + 4 x - 8$
5147	Find the Vertex	f(x)=4x^2-40x+107	$f (x) = 4 x^{2} - 40 x + 107$
5148	Find the Vertex	f(x)=6x^2+12x-1	$f (x) = 6 x^{2} + 12 x - 1$
5149	Find the Vertex	f(x)=6-2x+4x^2	$f (x) = 6 - 2 x + 4 x^{2}$
5150	Find the Vertex	g(x)=x^2-10x+20	$g (x) = x^{2} - 10 x + 20$
5151	Find the Vertex	g(x)=0.35x^2-3.5x-9	$g (x) = 0.35 x^{2} - 3.5 x - 9$
5152	Find the Vertex	g(x)=(x^2)/2+4x+6	$g (x) = \frac{x^{2}}{2} + 4 x + 6$
5153	Find the Vertex	f(x)=8x-x^2-12	$f (x) = 8 x - x^{2} - 12$
5154	Find the Vertex	f(x)=8x-x^2-15	$f (x) = 8 x - x^{2} - 15$
5155	Find the Vertex	g(x)=-x^2+4x+1	$g (x) = - x^{2} + 4 x + 1$
5156	Find the Vertex	g(x)=x^2+7x+12	$g (x) = x^{2} + 7 x + 12$
5157	Find the Vertex	f(x)=64t-16t^2	$f (x) = 64 t - 16 t^{2}$
5158	Find the Vertex	f(x)=3x^2+6x-1	$f (x) = 3 x^{2} + 6 x - 1$
5159	Find the Vertex	f(x)=4(x+1)^2-3	$f (x) = 4 {(x + 1)}^{2} - 3$
5160	Find the Vertex	f(x)=-3x^2-6x-1	$f (x) = - 3 x^{2} - 6 x - 1$
5161	Find the Vertex	f(x)=4(x-6)^2+3	$f (x) = 4 {(x - 6)}^{2} + 3$
5162	Find the Vertex	f(x)=4(x-2)^2-2	$f (x) = 4 {(x - 2)}^{2} - 2$
5163	Find the Vertex	f(x)=4x^2+24x+32	$f (x) = 4 x^{2} + 24 x + 32$
5164	Find the Vertex	f(x)=-4x^2+4x-1	$f (x) = - 4 x^{2} + 4 x - 1$
5165	Find the Vertex	f(x)=4x^2-32x-5	$f (x) = 4 x^{2} - 32 x - 5$
5166	Find the Vertex	f(x)=4x^2+80x-3	$f (x) = 4 x^{2} + 80 x - 3$
5167	Find the Vertex	f(x)=4x^2+8x+7	$f (x) = 4 x^{2} + 8 x + 7$
5168	Find the Vertex	f(x)=4x-x^2-3	$f (x) = 4 x - x^{2} - 3$
5169	Find the Vertex	g(x)=x^2-8x	$g (x) = x^{2} - 8 x$
5170	Find the Vertex	h(t)=18t-3t^2	$h (t) = 18 t - 3 t^{2}$
5171	Find the Vertex	h(x)=x^2-8x+16	$h (x) = x^{2} - 8 x + 16$
5172	Find the Vertex	h(x)=4x^2-4x+21	$h (x) = 4 x^{2} - 4 x + 21$
5173	Find the Vertex	k(x)=x^2+5x+4	$k (x) = x^{2} + 5 x + 4$
5174	Evaluate Using the Remainder Theorem	f(x)=2/3x+1 , f^-1(x)=(3x-3)/2	$f (x) = \frac{2}{3} x + 1$ , $f^{- 1} (x) = \frac{3 x - 3}{2}$
5175	Find the Vertex	f(x)=-2x^2+12x-3	$f (x) = - 2 x^{2} + 12 x - 3$
5176	Find the Vertex	f(x)=-2x^2+12x-9	$f (x) = - 2 x^{2} + 12 x - 9$
5177	Find the Vertex	f(x)=2x^2	$f (x) = 2 x^{2}$
5178	Find the Vertex	f(x)=1-x-x^2	$f (x) = 1 - x - x^{2}$
5179	Find the Vertex	f(x)=-2x^2+16x-31	$f (x) = - 2 x^{2} + 16 x - 31$
5180	Find the Vertex	f(x)=-2x^2+2x-3	$f (x) = - 2 x^{2} + 2 x - 3$
5181	Find the Vertex	f(x)=-2x^2+4x-7	$f (x) = - 2 x^{2} + 4 x - 7$
5182	Find the Vertex	f(x)=2x^2+4x-8	$f (x) = 2 x^{2} + 4 x - 8$
5183	Find the Vertex	f(x)=2x^2+4x-1	$f (x) = 2 x^{2} + 4 x - 1$
5184	Find the Vertex	f(x)=-2x^2+6x-1	$f (x) = - 2 x^{2} + 6 x - 1$
5185	Find the Vertex	f(x)=-2x^2+8x-13	$f (x) = - 2 x^{2} + 8 x - 13$
5186	Find the Vertex	f(x)=0.2x^2-0.5x-6.865	$f (x) = 0.2 x^{2} - 0.5 x - 6.865$
5187	Find the Vertex	f(x)=x^2-8x-2	$f (x) = x^{2} - 8 x - 2$
5188	Find the Vertex	f(x)=x^2-8x+12	$f (x) = x^{2} - 8 x + 12$
5189	Find the Vertex	f(x)=1-(x-3)^2	$f (x) = 1 - {(x - 3)}^{2}$
5190	Find the Vertex	f(x)=10x^2+5x-7	$f (x) = 10 x^{2} + 5 x - 7$
5191	Find the Vertex	f(x)=11.2t-16t^2	$f (x) = 11.2 t - 16 t^{2}$
5192	Find the Vertex	f(x)=16-(x-3)^2	$f (x) = 16 - {(x - 3)}^{2}$
5193	Find the Vertex	f(x)=2(x+3)^2-4	$f (x) = 2 {(x + 3)}^{2} - 4$
5194	Find the Vertex	f(x)=2x^2-8x+11	$f (x) = 2 x^{2} - 8 x + 11$
5195	Find the Vertex	f(x)=2x^2-8x+3	$f (x) = 2 x^{2} - 8 x + 3$
5196	Find the Vertex	f(x)=2x^2-7x+3	$f (x) = 2 x^{2} - 7 x + 3$
5197	Find the Vertex	f(x)=2x^2-5x+1	$f (x) = 2 x^{2} - 5 x + 1$
5198	Find the Vertex	f(x)=2x^2-4x-6	$f (x) = 2 x^{2} - 4 x - 6$
5199	Find the Vertex	f(x)=2x^2-6x-5/2	$f (x) = 2 x^{2} - 6 x - \frac{5}{2}$
5200	Find the Vertex	f(x)=2x^2-3x+1	$f (x) = 2 x^{2} - 3 x + 1$