mid range of 31/100 , 23/105 , 31/205 , 54/205

Topic

Full pad

`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

simplify solve for inverse tangent line

See All

area

asymptotes

critical points

derivative

domain

eigenvalues

eigenvectors

expand

extreme points

factor

implicit derivative

inflection points

intercepts

inverse

laplace

inverse laplace

partial fractions

range

slope

simplify

solve for

tangent

taylor

vertex

geometric test

alternating test

telescoping test

pseries test

root test

Steps Examples

Generated by AI

vertices (x+3)²=−20(y−1)

Solution

Maximum (−3, 1)

Show Steps

Hide Steps

Solve by:

Find vertex using polynomial form

Find vertex using parabola form

Find vertex using vertex form

Find vertex using averaging the zeros

One step at a time

(x+3)²=−20(y−1)

Parabola equation in polynomial form

The vertex of an up-down facing parabola of the form y=ax²+bx+c is x_v=−b2a

Rewrite (x+3)²=−20(y−1) in the form y=ax²+bx+c

y=−x²20 −3x10 −920 +1

The parabola parameters are:

a=−120 , b=−310 , c=−920 +1

x_v=−b2a

x_v=−(−310 )2(−120 )

Simplify −−310 2(−120 ) : −3

x_v=−3

Plug in x_v=−3 to find the y_v value

y_v=1

Therefore the parabola vertex is

(−3, 1)

If a<0, then the vertex is a maximum value
If a>0, then the vertex is a minimum value
a=−120

Maximum (−3, 1)

Examples

Popular topics

median calculator dot product calculator arc length calculator maclaurin series calculator z score calculator critical point calculator inequalities calculator range calculator determinant calculator second derivative calculator lcm calculator partial derivative calculator complete the square calculator distributive property calculator mixed fractions calculator Time Calculator gradient calculator triple integrals calculator partial fractions calculator indefinite integral calculator solve for x calculator double integral solver vector calculator Date Calculator vertex calculator binomial expansion calculator decimal to fraction calculator difference quotient calculator eigenvalue calculator piecewise functions calculator radius of convergence calculator roots calculator exponential function calculator interval of convergence calculator fractions divide calculator inflection point calculator expand calculator variance calculator fractions multiply calculator fourier series calculator foil calculator modulo calculator series convergence calculator linear algebra calculator

Chat with Symbo

Hi, ask a question about vertices (x+3)²=−20(y−1) or choose from the options below

Solve by: Find vertex using parabola form

Solve by: Find vertex using vertex form

Solve by: Find vertex using averaging the zeros

Cooking Calculators

Cooking Measurement Converter Cooking Ingredient Converter Cake Pan Converter More calculators

Fitness Calculators

BMI Calculator Calorie Calculator BMR Calculator More calculators

Notebook

View Full Notebook

−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

mid range of 31/100 , 23/105 , 31/205 , 54/205

Solution

Solution steps

Number Line

Graph