Find the Roots (Zeros) f(x)=-1/2(x-1)^2+2

$f (x) = - \frac{1}{2} {(x - 1)}^{2} + 2$

Set $- \frac{1}{2} \cdot {(x - 1)}^{2} + 2$ equal to $0$ .

$- \frac{1}{2} \cdot {(x - 1)}^{2} + 2 = 0$

Solve for $x$ .

Subtract $2$ from both sides of the equation.

$- \frac{1}{2} \cdot {(x - 1)}^{2} = - 2$

Combine ${(x - 1)}^{2}$ and $\frac{1}{2}$ .

$- \frac{{(x - 1)}^{2}}{2} = - 2$

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{{(x - 1)}^{2}}{2}) = - 2 \cdot - 2$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{{(x - 1)}^{2}}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{{(x - 1)}^{2}}{2}$ into the numerator.

$- 2 \frac{- {(x - 1)}^{2}}{2} = - 2 \cdot - 2$

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- {(x - 1)}^{2}}{2} = - 2 \cdot - 2$

Cancel the common factor.

$2 \cdot - 1 \frac{- {(x - 1)}^{2}}{2} = - 2 \cdot - 2$

Rewrite the expression.

$- - {(x - 1)}^{2} = - 2 \cdot - 2$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 {(x - 1)}^{2} = - 2 \cdot - 2$

Multiply ${(x - 1)}^{2}$ by $1$ .

${(x - 1)}^{2} = - 2 \cdot - 2$

Simplify the right side.

Multiply $- 2$ by $- 2$ .

${(x - 1)}^{2} = 4$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x - 1 = \pm \sqrt{4}$

Simplify $\pm \sqrt{4}$ .

Rewrite $4$ as $2^{2}$ .

$x - 1 = \pm \sqrt{2^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x - 1 = \pm 2$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x - 1 = 2$

Move all terms not containing $x$ to the right side of the equation.

Add $1$ to both sides of the equation.

$x = 2 + 1$

Add $2$ and $1$ .

$x = 3$

Next, use the negative value of the $\pm$ to find the second solution.

$x - 1 = - 2$

Move all terms not containing $x$ to the right side of the equation.

Add $1$ to both sides of the equation.

$x = - 2 + 1$

Add $- 2$ and $1$ .

$x = - 1$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 3, - 1$

Find the Roots (Zeros) f(x)=-1/2(x-1)^2+2

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