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# Quadratic functions & equations: FAQ

A quadratic is a type of function that can be written in the form $f\left(x\right)=a{x}^{2}+bx+c$, where $a$, $b$, and $c$ are constants.

## What is a parabola?

A parabola is the shape of the graph of a quadratic function. It looks like a symmetrical "U" shape, and can open either up or down depending on the function.
Practice with our Parabolas intro exercise.

## How are quadratic functions used in the real world?

Quadratic functions come up in a variety of real-world applications. For example, if we throw a ball into the air, the height of the ball as a function of time can be modeled with a quadratic function.

## What is the quadratic formula?

The quadratic formula is a formula we can use to solve any quadratic equation. It looks like this: $x=\frac{-b±\sqrt{{b}^{2}-4ac}}{2a}$, where $a$, $b$, and $c$ refer to the coefficients in a quadratic equation written in standard form: $a{x}^{2}+bx+c$.
Practice with our Quadratic formula exercise.

## What does "factored form" mean?

A quadratic equation is in factored form when it is written as a product of two linear factors. For example, $g\left(x\right)=\left(x+2\right)\left(x-3\right)$ is the factored form of $g\left(x\right)={x}^{2}-x-6$. The factored form is particularly useful, because we can set each factor equal to zero to find the $x$-intercepts of the graph of the function. For example, the graph of $g\left(x\right)$ has $x$ intercepts at $x=-2$ and $x=3$.

## What is vertex form?

Vertex form is another way of writing a quadratic equation. It looks like this: $f\left(x\right)=a\left(x-h{\right)}^{2}+k$, where $a$, $h$, and $k$ are constants. The vertex form is particularly useful for graphing quadratics because the vertex of the parabola is located at the point $\left(h,k\right)$.

## What does "completing the square" mean?

Completing the square is a technique we can use to rewrite a quadratic equation or function in a different form. We add and subtract terms to make one side of the equation look like a perfect square. This can help us solve the equation or graph the function.

## Why do we need to learn different methods for solving quadratic equations?

Different methods work better in different situations. For example, if a quadratic equation is already factored, solving it using factored form will usually be the easiest way to go. But if it's not factored, we might want to use the quadratic formula or complete the square.

## Want to join the conversation?

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Well, now I get to do a test, unit test and course test. Fun times.
• I can speak a bit of french. voila!
• How do you operate the graph on a quiz? I usually get the answers wrong when I have to graph a parabola. The reason is that when I want to put the dot on the y axis and the vertex is in the positive x area it won't allow me to. It lets me put the left hand dot on the vertex but then I have to move the right hand dot to intercept the y axis which is very inaccurate. It seems that it will only accept answers that have the dots over the vertex and the y intercept. But it won't let me. If I try to move the dot over the y intercept it reverses the parabola to the opposite orientation. How about some explanation of how to correctly graph a parabola using the tool. I usually know on paper where all the correct coordinates are and I would have the answer correct if only I could manipulate the graph. By the way, I keep putting questions and comments in this section but I get no response. How do I get help?
• This was always frustrating to me in the beginning because I understood the concept but couldn't get a correct answer. You have to play around with it a bit. I found graphing the vertex point first is best.
• At the top of the article, it says that "a quadratic is a type of function..." However, isn't a quadratic defined by its second-degree term? Quadratics can also be equations and expressions too, right; so how is a quadratic a type of function?
(1 vote)
• That's a good question. The graph of a quadratic function is a curve called a parabola. By using the straight line test (which is used to determine whether a graph represents a function), we can see that there is only ever one point on each vertical line drawn. This is why a quadratic is a type of function.