# Write an equation for a parabola given vertex and y intercept

Tips With all those letters and numbers floating around, it can be hard to know when you're "done" finding a formula!

Substitute a Substitute the value of a into the equation from Step 1. He has the unofficial record for the most undergraduate hours at the University of Texas at Austin.

Substitute in Coordinates for the Vertex Substitute the vertex's coordinates for h and k in the vertex form. You're told that the parabola's vertex is at the point 1,2that it opens vertically and that another point on the parabola is 3,5.

## How to write a quadratic equation with given roots and vertex

In math terms, a parabola the shape you get when you slice through a solid cone at an angle that's parallel to one of its sides, which is why it's known as one of the "conic sections. You're told that the parabola's vertex is at the point 1,2 , that it opens vertically and that another point on the parabola is 3,5. What is the equation of the parabola? For an example, let the vertex be 2, 3. Substitute a Substitute the value of a into the equation from Step 1. Tips Set either form to zero and solve the equation to find the points where the parabola crosses the x-axis. In this example, let the point be 3, 8. To do that choose any point x,y on the parabola, as long as that point is not the vertex, and substitute it into the equation. In either formula, the coordinates h,k represent the vertex of the parabola, which is the point where the parabola's axis of symmetry crosses the line of the parabola itself. Substitute in the Vertex Next, substitute the parabola's vertex coordinates h, k into the formula you chose in Step 1. Substitute in Coordinates for the Vertex Substitute the vertex's coordinates for h and k in the vertex form. Imagine that you're given a parabola in graph form.

Imagine that you're given a parabola in graph form. Determine Whether It's Horizontal or Vertical Your very first priority has to be deciding which form of the vertex equation you'll use.

Parabolas have two equation forms — standard and vertex. In either formula, the coordinates h,k represent the vertex of the parabola, which is the point where the parabola's axis of symmetry crosses the line of the parabola itself.

With just two of the parabola's points, its vertex and one other, you can find a parabolic equation's vertex and standard forms and write the parabola algebraically.

### Write an equation for a parabola given vertex and y intercept

Once you have this information, you can find the equation of the parabola in three steps. In either formula, the coordinates h,k represent the vertex of the parabola, which is the point where the parabola's axis of symmetry crosses the line of the parabola itself. These variables are usually written as x and y, especially when you're dealing with "standardized" shapes such as a parabola. As a general rule, when you're working with problems in two dimensions, you're done when you have only two variables left. For an example, let the vertex be 2, 3. Imagine that you're given a parabola in graph form. Substitute in Coordinates for the Vertex Substitute the vertex's coordinates for h and k in the vertex form. In math terms, a parabola the shape you get when you slice through a solid cone at an angle that's parallel to one of its sides, which is why it's known as one of the "conic sections. Determine Whether It's Horizontal or Vertical Your very first priority has to be deciding which form of the vertex equation you'll use. Finding the Equation of a Parabola If you're being asked to find the equation of a parabola, you'll either be told the vertex of the parabola and at least one other point on it, or you'll be given enough information to figure those out. Substitute a Substitute the value of a into the equation from Step 1. In this example, let the point be 3, 8. Convert to Standard Form Square the expression inside the parentheses, multiply the terms by a's value and combine like terms to convert the equation to standard form.

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