Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
105201	Find the Vertex	y=1/2x^2-2x+1	$y = \frac{1}{2} x^{2} - 2 x + 1$
105202	Determine the Possible Number of Real Roots	f(x)=11x^5+5x+25	$f (x) = 11 x^{5} + 5 x + 25$
105203	Find the Vertex	y=-1/2x^2-1	$y = - \frac{1}{2} x^{2} - 1$
105204	Determine the Possible Number of Real Roots	f(x)=15x^23+41x^19+13x^5-10	$f (x) = 15 x^{23} + 41 x^{19} + 13 x^{5} - 10$
105205	Find the Vertex	y=1/2x^2+4x+5	$y = \frac{1}{2} x^{2} + 4 x + 5$
105206	Determine the Possible Number of Real Roots	f(x)=15x^4-x^2+9	$f (x) = 15 x^{4} - x^{2} + 9$
105207	Determine the Possible Number of Real Roots	f(x)=16x^4-112x^3+235x^2-114x-45	$f (x) = 16 x^{4} - 112 x^{3} + 235 x^{2} - 114 x - 45$
105208	Determine the Possible Number of Real Roots	f(x)=17x^15+41x^12+13x^3-10	$f (x) = 17 x^{15} + 41 x^{12} + 13 x^{3} - 10$
105209	Determine the Possible Number of Real Roots	f(x)=21x^5-6x^3+8x+9	$f (x) = 21 x^{5} - 6 x^{3} + 8 x + 9$
105210	Find the Vertex	y=x^2+10x-27	$y = x^{2} + 10 x - 27$
105211	Find the Vertex	y=-x^2+12x-20	$y = - x^{2} + 12 x - 20$
105212	Determine the Possible Number of Real Roots	f(x)=2x^5-2x^2+x-2	$f (x) = 2 x^{5} - 2 x^{2} + x - 2$
105213	Find the Vertex	y=x^2+4x+11	$y = x^{2} + 4 x + 11$
105214	Find the Vertex	y=x^2+3x-6	$y = x^{2} + 3 x - 6$
105215	Determine the Possible Number of Real Roots	f(x)=2x^5-4x^2+x-1	$f (x) = 2 x^{5} - 4 x^{2} + x - 1$
105216	Find the Vertex	y=x^2+5x-14	$y = x^{2} + 5 x - 14$
105217	Determine the Possible Number of Real Roots	f(x)=3x^4+5x^3-12x^2-9x-5	$f (x) = 3 x^{4} + 5 x^{3} - 12 x^{2} - 9 x - 5$
105218	Find the Vertex	y=x^2+6x-2	$y = x^{2} + 6 x - 2$
105219	Determine the Possible Number of Real Roots	f(x)=3x^4-7x^3+x^2-x+1	$f (x) = 3 x^{4} - 7 x^{3} + x^{2} - x + 1$
105220	Find the Vertex	y=x^2+6x-16	$y = x^{2} + 6 x - 16$
105221	Determine the Possible Number of Real Roots	f(x)=3x^5-4x^2+x-3	$f (x) = 3 x^{5} - 4 x^{2} + x - 3$
105222	Find the Vertex	y=-x^2+8x-18	$y = - x^{2} + 8 x - 18$
105223	Determine the Possible Number of Real Roots	f(x)=49x^4-9x^3+6x+14	$f (x) = 49 x^{4} - 9 x^{3} + 6 x + 14$
105224	Find the Vertex	y=x^2-10x-2	$y = x^{2} - 10 x - 2$
105225	Determine the Possible Number of Real Roots	f(x)=4x^5-8x^4-5x^3+10x^2+x-2	$f (x) = 4 x^{5} - 8 x^{4} - 5 x^{3} + 10 x^{2} + x - 2$
105226	Find the Vertex	y=x^2-10x+15	$y = x^{2} - 10 x + 15$
105227	Determine the Possible Number of Real Roots	f(x)=5x^3+27x^2+11x+5	$f (x) = 5 x^{3} + 27 x^{2} + 11 x + 5$
105228	Find the Vertex	y=-x^2-10x	$y = - x^{2} - 10 x$
105229	Determine the Possible Number of Real Roots	f(x)=6x^4-4x^3-3x+2	$f (x) = 6 x^{4} - 4 x^{3} - 3 x + 2$
105230	Find the Vertex	y=x^2-10x	$y = x^{2} - 10 x$
105231	Determine the Possible Number of Real Roots	f(x)=6x^5-2x^3+8x+20	$f (x) = 6 x^{5} - 2 x^{3} + 8 x + 20$
105232	Find the Vertex	y=(x+5)(x+3)	$y = (x + 5) (x + 3)$
105233	Determine the Possible Number of Real Roots	f(x)=6x^6-10x^5+x^4-3x^3+20	$f (x) = 6 x^{6} - 10 x^{5} + x^{4} - 3 x^{3} + 20$
105234	Find the Vertex	y=(x+5)(x-1)	$y = (x + 5) (x - 1)$
105235	Determine the Possible Number of Real Roots	f(x)=-7x^5-6x^4-3x^3+6x^2+x+12	$f (x) = - 7 x^{5} - 6 x^{4} - 3 x^{3} + 6 x^{2} + x + 12$
105236	Find the Vertex	x^2=-4y	$x^{2} = - 4 y$
105237	Determine the Possible Number of Real Roots	f(x)=8x^4-58x^3+129x^2-72x-27	$f (x) = 8 x^{4} - 58 x^{3} + 129 x^{2} - 72 x - 27$
105238	Determine the Possible Number of Real Roots	f(x)=8x^5-4x^3+6x+15	$f (x) = 8 x^{5} - 4 x^{3} + 6 x + 15$
105239	Determine the Possible Number of Real Roots	f(x)=9x^3+9x^2-4x-4	$f (x) = 9 x^{3} + 9 x^{2} - 4 x - 4$
105240	Find the Vertex	y=2x-x^2	$y = 2 x - x^{2}$
105241	Determine the Possible Number of Real Roots	f(x)=-9x^7+x^5-x^2+4	$f (x) = - 9 x^{7} + x^{5} - x^{2} + 4$
105242	Find the Vertex	y=-2x^2-4x-5	$y = - 2 x^{2} - 4 x - 5$
105243	Find the Vertex	y=-2x^2-4x+1	$y = - 2 x^{2} - 4 x + 1$
105244	Find the Vertex	y=2x^2-5x-12	$y = 2 x^{2} - 5 x - 12$
105245	Determine the Possible Number of Real Roots	f(x)=x^3+3x^2-219x-221	$f (x) = x^{3} + 3 x^{2} - 219 x - 221$
105246	Find the Vertex	y=2x^2-8x-10	$y = 2 x^{2} - 8 x - 10$
105247	Find the Vertex	y=-2x^2-4	$y = - 2 x^{2} - 4$
105248	Find the Vertex	y=2x^2-16x+34	$y = 2 x^{2} - 16 x + 34$
105249	Determine the Possible Number of Real Roots	f(x)=x^3+9x^2+8x+7	$f (x) = x^{3} + 9 x^{2} + 8 x + 7$
105250	Find the Vertex	y=2x^2+4x-4	$y = 2 x^{2} + 4 x - 4$
105251	Find the Vertex	y=2x^2+4x-8	$y = 2 x^{2} + 4 x - 8$
105252	Determine the Possible Number of Real Roots	f(x)=x^3-11x+20	$f (x) = x^{3} - 11 x + 20$
105253	Find the Vertex	y=2x^2+8x-2	$y = 2 x^{2} + 8 x - 2$
105254	Determine the Possible Number of Real Roots	f(x)=x^3-5x^2-61x-55	$f (x) = x^{3} - 5 x^{2} - 61 x - 55$
105255	Find the Vertex	y=-2x^2+8x-9	$y = - 2 x^{2} + 8 x - 9$
105256	Find the Vertex	y=2x^2+8x+4	$y = 2 x^{2} + 8 x + 4$
105257	Find the Vertex	y=2x^2+8x+10	$y = 2 x^{2} + 8 x + 10$
105258	Find the Vertex	y=-2x^2-12x-23	$y = - 2 x^{2} - 12 x - 23$
105259	Determine the Possible Number of Real Roots	f(x)=x^4+7x^3+3x^2-63x-108	$f (x) = x^{4} + 7 x^{3} + 3 x^{2} - 63 x - 108$
105260	Find the Vertex	y=2x^2+x	$y = 2 x^{2} + x$
105261	Determine the Possible Number of Real Roots	f(x)=x^4-3x^3+6x^2+2x-60	$f (x) = x^{4} - 3 x^{3} + 6 x^{2} + 2 x - 60$
105262	Find the Vertex	y=-2x^2+12x-15	$y = - 2 x^{2} + 12 x - 15$
105263	Determine the Possible Number of Real Roots	f(x)=x^4-4x^3-18x^2+108x-135	$f (x) = x^{4} - 4 x^{3} - 18 x^{2} + 108 x - 135$
105264	Find the Vertex	y=2x^2+16x+35	$y = 2 x^{2} + 16 x + 35$
105265	Find the Vertex	y=-2x^2+16x-15	$y = - 2 x^{2} + 16 x - 15$
105266	Find the Vertex	y=-x^2-5x	$y = - x^{2} - 5 x$
105267	Find the Vertex	y=x^2-3x-18	$y = x^{2} - 3 x - 18$
105268	Find the Vertex	y=x^2-4x+11	$y = x^{2} - 4 x + 11$
105269	Determine the Possible Number of Real Roots	h(x)=2x^6-4x^5+3x^4-8x^3+x^2-6x+11	$h (x) = 2 x^{6} - 4 x^{5} + 3 x^{4} - 8 x^{3} + x^{2} - 6 x + 11$
105270	Find the Vertex	y=x^2-2x-323	$y = x^{2} - 2 x - 323$
105271	Determine the Possible Number of Real Roots	p(x)=(x^2+6x+9)(x+3)	$p (x) = (x^{2} + 6 x + 9) (x + 3)$
105272	Find the Vertex	y=x^2-18	$y = x^{2} - 18$
105273	Find the Vertex	y=x^2-20x+105	$y = x^{2} - 20 x + 105$
105274	Determine the Possible Number of Real Roots	p(x)=4x^5+8x^3+x+5	$p (x) = 4 x^{5} + 8 x^{3} + x + 5$
105275	Find the Vertex	y=x^2-6x-1	$y = x^{2} - 6 x - 1$
105276	Determine the Possible Number of Real Roots	p(x)=8x^3+2x^2-14x+5	$p (x) = 8 x^{3} + 2 x^{2} - 14 x + 5$
105277	Find the Vertex	y=x^2-8x+14	$y = x^{2} - 8 x + 14$
105278	Determine the Possible Number of Real Roots	p(x)=x^4-5x^3+2x^2+10x-8	$p (x) = x^{4} - 5 x^{3} + 2 x^{2} + 10 x - 8$
105279	Find the Vertex	y=x^2-7x+18	$y = x^{2} - 7 x + 18$
105280	Determine the Possible Number of Real Roots	p(x)=x^5+3x^3+2x-6	$p (x) = x^{5} + 3 x^{3} + 2 x - 6$
105281	Find the Vertex	y=x^2-6x-9	$y = x^{2} - 6 x - 9$
105282	Find the Vertex	y=x^2-9x	$y = x^{2} - 9 x$
105283	Find the Vertex	y=-2(x+3)^2+2	$y = - 2 {(x + 3)}^{2} + 2$
105284	Find the Other Trig Values in Quadrant II	square root of 3cot(theta)-1=0	$\sqrt{3} \cot (θ) - 1 = 0$
105285	Find the Vertex	y=7-x^2	$y = 7 - x^{2}$
105286	Find the Vertex	y=-8x^2+3	$y = - 8 x^{2} + 3$
105287	Find the Vertex	y=3x^2-12x+15	$y = 3 x^{2} - 12 x + 15$
105288	Find the Vertex	y=3x^2-18x+24	$y = 3 x^{2} - 18 x + 24$
105289	Find the Vertex	y=3x^2-4x+5	$y = 3 x^{2} - 4 x + 5$
105290	Find the Vertex	y=-3x^2-6x+7	$y = - 3 x^{2} - 6 x + 7$
105291	Find the Vertex	y=3x^2-6x-5	$y = 3 x^{2} - 6 x - 5$
105292	Find the Vertex	y=3x^2+6x-4	$y = 3 x^{2} + 6 x - 4$
105293	Find the Other Trig Values in Quadrant II	2sin(x)^2-5sin(x)+2=0	$2 \sin^{2} (x) - 5 \sin (x) + 2 = 0$
105294	Find the Other Trig Values in Quadrant II	-2sin(x)^2-sin(x)+1=0	$- 2 \sin^{2} (x) - \sin (x) + 1 = 0$
105295	Find the Vertex	y=3x^2+6	$y = 3 x^{2} + 6$
105296	Find the Vertex	y=4x^2+24x+38	$y = 4 x^{2} + 24 x + 38$
105297	Find the Other Trig Values in Quadrant II	3cos(x)^2-3sin(x)^2=0	$3 \cos^{2} (x) - 3 \sin^{2} (x) = 0$
105298	Find the Vertex	y=4x^2+7	$y = 4 x^{2} + 7$
105299	Find the Vertex	y=4x^2+7x	$y = 4 x^{2} + 7 x$
105300	Find the Vertex	y=4x^2+16x+13	$y = 4 x^{2} + 16 x + 13$