Solve the equation $y=3x^2+2x+1$

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Final answer to the problem

$y=\frac{9\left(x+\frac{1}{3}\right)^2+2}{3}$
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Step-by-step Solution

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Apply the formula: $ax^2+bx+c$$=a\left(x^2+\frac{b}{a}x+\frac{c}{a}\right)$, where $a=3$, $b=2$ and $c=1$

$y=3\left(x^2+\frac{2}{3}x+\frac{1}{3}\right)$

Learn how to solve equazioni problems step by step online.

$y=3\left(x^2+\frac{2}{3}x+\frac{1}{3}\right)$

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Learn how to solve equazioni problems step by step online. Solve the equation y=3x^2+2x+1. Apply the formula: ax^2+bx+c=a\left(x^2+\frac{b}{a}x+\frac{c}{a}\right), where a=3, b=2 and c=1. Apply the formula: a\left(x^2+b+c\right)=a\left(x^2+b+c+\left(\frac{coef\left(b\right)}{2}\right)^2-\left(\frac{coef\left(b\right)}{2}\right)^2\right), where a=3, b=\frac{2}{3}x and c=\frac{1}{3}. Apply the formula: a\left(x^2+b+c+f+g\right)=a\left(\left(x+\sqrt{f}sign\left(b\right)\right)^2+c+g\right), where a=3, b=\frac{2}{3}x, c=\frac{1}{3}, x^2+b=x^2+\frac{2}{3}x+\frac{1}{3}+\frac{1}{9}-\frac{1}{9}, f=\frac{1}{9} and g=-\frac{1}{9}. The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors.

Final answer to the problem

$y=\frac{9\left(x+\frac{1}{3}\right)^2+2}{3}$

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Function Plot

Plotting: $y-3x^2-2x-1$

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7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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