# Finding parabola equation and only given a graph

In summary, To find an equation for a given graph, use the vertex form y = a(x + h)^2 + k, where h is the x-value of the vertex and k is the y-value. This formula can be used for all parabolas with a vertical axis.

## Homework Statement

The math problem I am supposed to do is, find an equation for the given graph.

## Homework Equations

There are no equations given, but here's an image for it.

## The Attempt at a Solution

I understand there is an equation like
y=ax^2+bx+c but I'm not sure how I can apply it to this graph. I know the Vertex of the Parabola is (0,5) and the line of symmetry I think it's called is x=0, but what I'm confused at is what the actual equation would be.

If anyone can give me a clue as how I can solve it, that would be great!

Put it in vertex form $$y = a(x + h)^2 + k$$ where h is the x value of the vertex and k is the y value. The answer should then be $$y = ax^2 + 5$$, you can solve for a by plugging in values of x, y and then isolate a, there is a clear one $$(1, 4)$$. I don't know if I can give this much information though.

Wow, I'm impressed this was answered so quickly! Thanks!
So is this a standard equation that can be used for solving all parabola's?

Wow, I'm impressed this was answered so quickly! Thanks!
So is this a standard equation that can be used for solving all parabola's?
Especially at 1 AM!

Yes, that formula is true for all parabolas with vertical axis.

## 1. What is a parabola?

A parabola is a symmetrical curve that is shaped like an arch. It is a type of conic section, meaning it is created by the intersection of a plane and a cone.

## 2. How do I find the equation of a parabola given a graph?

To find the equation of a parabola given a graph, you will need to identify the vertex and at least two other points on the curve. Then, you can use the general form of the parabola equation (y = ax^2 + bx + c) and plug in the coordinates of the vertex and the two other points to solve for the values of a, b, and c.

## 3. What if I only have one point on the parabola?

If you only have one point on the parabola, you will not be able to find the exact equation of the curve. However, you can use the point-slope form of a line to create an equation that approximates the parabola. This will not give you the exact curve, but it will give you an idea of the general shape and direction of the parabola.

## 4. Can I use a calculator to find the equation of a parabola?

Yes, there are many online calculators and graphing tools that can help you find the equation of a parabola given a graph. However, it is important to understand the steps and concepts involved in finding the equation in case you do not have access to a calculator or need to solve a similar problem by hand.

## 5. Are there other ways to find the equation of a parabola?

Yes, there are other methods for finding the equation of a parabola, such as using the focus and directrix, or using the distance formula. These methods may be more advanced and require a deeper understanding of parabolas and algebra, but they can also be useful tools in certain situations.