Solve the System of Equations y=x^2-2x+4 y=-x^2-2x+4

$y = x^{2} - 2 x + 4$ $y = - x^{2} - 2 x + 4$

Eliminate the equal sides of each equation and combine.

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

Solve $x^{2} - 2 x + 4 = - x^{2} - 2 x + 4$ for $x$ .

Move all terms containing $x$ to the left side of the equation.

Add $x^{2}$ to both sides of the equation.

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

Add $2 x$ to both sides of the equation.

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

Combine the opposite terms in $x^{2} - 2 x + 4 + x^{2} + 2 x$ .

Add $- 2 x$ and $2 x$ .

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

Add $x^{2} + 4 + x^{2}$ and $0$ .

$x^{2} + 4 + x^{2} = 4$

Add $x^{2}$ and $x^{2}$ .

$2 x^{2} + 4 = 4$

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

Subtract $4$ from both sides of the equation.

$2 x^{2} = 4 - 4$

Subtract $4$ from $4$ .

$2 x^{2} = 0$

Divide each term in $2 x^{2} = 0$ by $2$ and simplify.

Divide each term in $2 x^{2} = 0$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{0}{2}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$x^{2} = 0$

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

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

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

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$

Evaluate $y$ when $x = 0$ .

Substitute $0$ for $x$ .

$y = - {(0)}^{2} - 2 \cdot 0 + 4$

Substitute $0$ for $x$ in $y = - {(0)}^{2} - 2 \cdot 0 + 4$ and solve for $y$ .

Remove parentheses.

$y = - 0^{2} - 2 \cdot 0 + 4$

Remove parentheses.

$y = - {(0)}^{2} - 2 \cdot 0 + 4$

Simplify $- {(0)}^{2} - 2 \cdot 0 + 4$ .

Simplify each term.

Raising $0$ to any positive power yields $0$ .

$y = - 0 - 2 \cdot 0 + 4$

Multiply $- 1$ by $0$ .

$y = 0 - 2 \cdot 0 + 4$

Multiply $- 2$ by $0$ .

$y = 0 + 0 + 4$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 4$

Add $0$ and $4$ .

$y = 4$

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(0, 4)$

The result can be shown in multiple forms.

Point Form:

$(0, 4)$

Equation Form:

$x = 0, y = 4$

Solve the System of Equations y=x^2-2x+4 y=-x^2-2x+4

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