Find the Points of Intersection y=x^2 , y=x+2

$y = x^{2}$ , $y = x + 2$

Substitute $x^{2}$ for $y$ into $y = x + 2$ then solve for $x$ .

Tap for more steps…

Replace $y$ with $x^{2}$ in the equation.

$x^{2} = x + 2$

Solve the equation for $x$ .

Tap for more steps…

Subtract $x$ from both sides of the equation.

$x^{2} - x = 2$

Move $2$ to the left side of the equation by subtracting it from both sides.

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

Factor $x^{2} - x - 2$ using the AC method.

Tap for more steps…

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 2$ and whose sum is $- 1$ .

$- 2, 1$

Write the factored form using these integers.

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

Set $x - 2$ equal to $0$ and solve for $x$ .

Tap for more steps…

Set the factor equal to $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Set $x + 1$ equal to $0$ and solve for $x$ .

Tap for more steps…

Set the factor equal to $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

The solution is the result of $x - 2 = 0$ and $x + 1 = 0$ .

$x = 2, - 1$

Substitute $2$ for $x$ into $y = x + 2$ then solve for $y$ .

Tap for more steps…

Replace $x$ with $2$ in the equation.

$x = 2$

$y = (2) + 2$

Solve the equation for $y$ .

Tap for more steps…

Remove the parentheses around the expression $2$ .

$y = 2 + 2$

Add $2$ and $2$ .

$y = 4$

Substitute $- 1$ for $x$ into $y = x + 2$ then solve for $y$ .

Tap for more steps…

Replace $x$ with $- 1$ in the equation.

$x = - 1$

$y = (- 1) + 2$

Solve the equation for $y$ .

Tap for more steps…

Remove the parentheses around the expression $- 1$ .

$y = - 1 + 2$

Add $- 1$ and $2$ .

$y = 1$

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

$(2, 4), (- 1, 1)$

Find the Points of Intersection y=x^2 , y=x+2

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our
App from the store