Find a,b,c (x-1)^2+3=2x+1

${(x - 1)}^{2} + 3 = 2 x + 1$

Step 1

Move all terms to the left side of the equation and simplify.

Move all the expressions to the left side of the equation.

Subtract $2 x$ from both sides of the equation.

${(x - 1)}^{2} + 3 - 2 x = 1$

Subtract $1$ from both sides of the equation.

${(x - 1)}^{2} + 3 - 2 x - 1 = 0$

Simplify ${(x - 1)}^{2} + 3 - 2 x - 1$ .

Simplify each term.

Rewrite ${(x - 1)}^{2}$ as $(x - 1) (x - 1)$ .

$(x - 1) (x - 1) + 3 - 2 x - 1 = 0$

Expand $(x - 1) (x - 1)$ using the FOIL Method.

Apply the distributive property.

$x (x - 1) - 1 (x - 1) + 3 - 2 x - 1 = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 1 - 1 (x - 1) + 3 - 2 x - 1 = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1 + 3 - 2 x - 1 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 1 - 1 x - 1 \cdot - 1 + 3 - 2 x - 1 = 0$

Move $- 1$ to the left of $x$ .

$x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1 + 3 - 2 x - 1 = 0$

Rewrite $- 1 x$ as $- x$ .

$x^{2} - x - 1 x - 1 \cdot - 1 + 3 - 2 x - 1 = 0$

Rewrite $- 1 x$ as $- x$ .

$x^{2} - x - x - 1 \cdot - 1 + 3 - 2 x - 1 = 0$

Multiply $- 1$ by $- 1$ .

$x^{2} - x - x + 1 + 3 - 2 x - 1 = 0$

Subtract $x$ from $- x$ .

$x^{2} - 2 x + 1 + 3 - 2 x - 1 = 0$

Combine the opposite terms in $x^{2} - 2 x + 1 + 3 - 2 x - 1$ .

Subtract $1$ from $1$ .

$x^{2} - 2 x + 3 - 2 x + 0 = 0$

Add $x^{2} - 2 x + 3 - 2 x$ and $0$ .

$x^{2} - 2 x + 3 - 2 x = 0$

Subtract $2 x$ from $- 2 x$ .

$x^{2} - 4 x + 3 = 0$

Step 2

Once the quadratic is in standard form, the values of $a$ , $b$ , and $c$ can be found.

$a x^{2} + b x + c$

Step 3

Use the standard form of the equation to find $a$ , $b$ , and $c$ for this quadratic.

$a = 1$ , $b = - 4$ , $c = 3$

Find a,b,c (x-1)^2+3=2x+1

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