# Precalculus : Determine the Equation of a Parabola in Standard Form

## Example Questions

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### Example Question #1485 : Pre Calculus

Express the following equation for a parabola in standard form:

Explanation:

In order to be in standard form, the equation for a parabola must be written in one of the following ways:

We can see that our equation has all of the components of the first form above, so now all we must do is some algebra to rearrange the equation and express the function y in terms of x. We start by simplifying the fraction on the left side of the equation, and then we isolate y to give us the equation of the parabola in standard form:

### Example Question #1 : Determine The Equation Of A Parabola In Standard Form

Rewrite  in standard form.

Explanation:

The standard form of a parabola is .

Factorize the right side of , and simplify.

### Example Question #2 : Determine The Equation Of A Parabola In Standard Form

If the vertex of the parabola is , and the y-intercept is , find the equation of the parabola, if possible.

Explanation:

First, write the equation of the parabola in standard form.

Determine the values of the coefficients.  The value of the y-intercept is 4, which means that .

Write the vertex formula.

The given point of the vertex is , which indicates that:

Substitute the value of the point and  into the standard form.

Substitute this value into  to determine the value of .

Substitute the values of  coefficients into the standard form of the parabola.

### Example Question #3 : Determine The Equation Of A Parabola In Standard Form

Find the standard form of the equation of the following parabola:

Explanation:

Recall the standard equation of a horizontal parabola:

, where  is the vertex and  is the focal length.

Start by isolating the  terms.

Complete the square on the left. Make sure to add the same amount to both sides of the equation!

Factor both sides of the equation to get the standard form of a horizontal parabola.

### Example Question #4 : Determine The Equation Of A Parabola In Standard Form

Find the standard form of equation of the following parabola:

Explanation:

Recall the standard equation of a horizontal parabola:

, where  is the vertex and  is the focal length.

Start by isolating the  terms.

Complete the square on the left. Make sure to add the same amount to both sides of the equation!

Factor both sides of the equation to get the standard form of a horizontal parabola.

### Example Question #5 : Determine The Equation Of A Parabola In Standard Form

Find the standard form of the equation for the following parabola:

Explanation:

Recall the standard equation of a horizontal parabola:

, where  is the vertex and  is the focal length.

Start by isolating the  terms.

Complete the square on the left. Make sure to add the same amount to both sides of the equation!

Factor both sides of the equation to get the standard form of a horizontal parabola.

### Example Question #6 : Determine The Equation Of A Parabola In Standard Form

Find the standard form of the equation for the following parabola:

Explanation:

Recall the standard equation of a vertical parabola:

, where  is the vertex and  is the focal length.

Start by isolating the  terms.

Complete the square on the left. Make sure to add the same amount to both sides of the equation!

Factor both sides of the equation to get the standard form of a vertical parabola.

### Example Question #7 : Determine The Equation Of A Parabola In Standard Form

Find the standard form of the equation for the following parabola:

Explanation:

Recall the standard equation of a vertical parabola:

, where  is the vertex and  is the focal length.

Start by isolating the  terms.

Complete the square on the left. Make sure to add the same amount to both sides of the equation!

Factor both sides of the equation to get the standard form of a vertical parabola.

### Example Question #8 : Determine The Equation Of A Parabola In Standard Form

Find the standard form of the equation for the following parabola:

Explanation:

Recall the standard equation of a vertical parabola:

, where  is the vertex and  is the focal length.

Start by isolating the  terms.

Complete the square on the left. Make sure to add the same amount to both sides of the equation!

Factor both sides of the equation to get the standard form of a vertical parabola.

### Example Question #9 : Determine The Equation Of A Parabola In Standard Form

Find the standard form of the equation of a parabola with the following equation:

Explanation:

Recall the standard equation of a vertical parabola:

, where  is the vertex and  is the focal length.

Start by isolating the  terms.

Complete the square on the left. Make sure to add the same amount to both sides of the equation!

Factor both sides of the equation to get the standard form of a vertical parabola.

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