# Write an equation in standard form of the parabola opens

Let's begin by looking at the standard form for the equation of a parabola.

### Transformational form equation of a parabola

Looks like hairy spider legs! When completing the square, we first have to isolate the Ax2 term and the By term from the C term. Let's begin by looking at the standard form for the equation of a parabola. Once we have identified what the y-coordinate is, the last question we have is whether this number represents a maximum or minimum. Example 2 Let's now look at an example of another equation of a parabola in standard form. Completing the square to get the standard form of a parabola. By adding 4 to the inside of the parenthesis, we have done more than just add 4 to the equation. The vertex is shifted off of the origin, and we need to consider the h and k terms. What is the equation of the parabola?

Tips With all those letters and numbers floating around, it can be hard to know when you're "done" finding a formula! For some supplementary exercises over what we have covered in lesson 2, click here: Exercise 2 Lesson 3 Find the equation of a parabola when we are given the coordinates of its focus and vertex.

These parabolas are considered relations.

### Parabola equation examples

Factor and simplify. Updated November 19, By Lisa Maloney In real-world terms, a parabola is the arc a ball makes when you throw it, or the distinctive shape of a satellite dish. This is what our 4p term is equal to. The plus sign that is directly under the vertex is the focus. Up if a is positive, down if a is negative h, k The multiplier 4a is a constant that tells you how steep or wide the parabola is. With this in mind, the line of symmetry also known as the axis of symmetry is the line that splits the parabola into two separate branches that mirror each other. A great deal can be determined by an equation in this form. We will stick to what we've been doing all along and put the isolated terms on the left. The picture below shows this parabola in the first quadrant. So, really we are adding 12 to the equation, and we must now offset that on the same side of the equation. The term in front of the x is a If you have GSP, click here. Let's take a look.

We will now go into a bit of detail as to how to derive all of this information from a given equation. Not always do we come up on equations that are there just waiting for us to solve them.

Let's now take a look at a parabola that has all of the elements that we will be looking for: the vertex the focus the directrix The following example is especially meant for those who do not have GSP on your computer.

The term in front of the x is a This definition may be hard to visualize. Notice that you have to add 98 to the right, because the 49 that you added to complete the square is multiplied by 2. Following are answers to the practice questions: 1.

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