Algebra Examples

Find the Parabola Through (3,6) with Vertex (1,-2)
,
The general equation of a parabola with vertex is . In this case we have as the vertex and is a point on the parabola. To find , substitute the two points in to get .
Using to solve for , .
Tap for more steps...
Rewrite the equation as .
Simplify each term.
Tap for more steps...
Multiply by to get .
Subtract from to get .
Remove parentheses around .
Raise to the power of to get .
Move to the left of the expression .
Multiply by to get .
Move all terms not containing to the right side of the equation.
Tap for more steps...
Since does not contain the variable to solve for, move it to the right side of the equation by adding to both sides.
Add and to get .
Divide each term by and simplify.
Tap for more steps...
Divide each term in by .
Reduce the expression by cancelling the common factors.
Tap for more steps...
Cancel the common factor.
Divide by to get .
Divide by to get .
Using , the general equation of the parabola with the vertex and is .
Solve for to get .
Tap for more steps...
Remove the extra parentheses.
Remove the parentheses around the expression .
Simplify each term.
Tap for more steps...
Multiply by to get .
Rewrite as .
Expand using the FOIL Method.
Tap for more steps...
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Remove parentheses.
Simplify and combine like terms.
Tap for more steps...
Simplify each term.
Tap for more steps...
Use the power rule to combine exponents.
Add and to get .
Move to the left of the expression .
Multiply by to get .
Rewrite as .
Rewrite as .
Multiply by to get .
Subtract from to get .
Apply the distributive property.
Simplify.
Tap for more steps...
Multiply by to get .
Multiply by to get .
Simplify by subtracting numbers.
Tap for more steps...
Subtract from to get .
Add and to get .
The standard form and vertex form are as follows.
Standard Form:
Vertex Form:
Simplify the standard form.
Standard Form:
Vertex Form:
Enter YOUR Problem

Enter the email address associated with your Mathway account below and we'll send you a link to reset your password.

Please enter an email address
Please enter a valid email address
The email address you entered was not found in our system
The email address you entered is associated with a Facebook user
We're sorry, we were unable to process your request at this time

Mathway Premium

Step-by-step work + explanations
  •    Step-by-step work
  •    Detailed explanations
  •    No advertisements
  •    Access anywhere
Access the steps on both the Mathway website and mobile apps
$--.--/month
$--.--/year (--%)

Mathway Premium

Visa and MasterCard security codes are located on the back of card and are typically a separate group of 3 digits to the right of the signature strip.

American Express security codes are 4 digits located on the front of the card and usually towards the right.
This option is required to subscribe.
Go Back

Step-by-step upgrade complete!

Mathway requires javascript and a modern browser.
  [ x 2     1 2     π     x d x   ]