### Quadratic formula explained (article) | Khan Academy

The relationship between variables determines how the right conclusions are reached. Science Projects for Kids, Survey Guide, Philosophy of Science, Reasoning, Ethics This means you need to establish how the variables are related - is the relationship linear or quadratic or inverse or logarithmic or something else?. In an inverse relationship, instead of the two variables moving in the same direction they move in opposite directions, meaning as one variable. The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant tells us Discriminant review. CCSS Math.

An example might involve building a rectangular box where one side must be twice the length of the other side.

## Understanding the quadratic formula

For example, if you have only 4 square feet of wood to use for the bottom of the box, with this information, you can create an equation for the area of the box using the ratio of the two sides.

This equation must be less than or equal to four to successfully make a box using these constraints.

- Relationships in Physical and Social Sciences
- This article is a part of the guide:
- The quadratic formula

Figuring a Profit Sometimes calculating a business profit requires using a quadratic function. If you want to sell something — even something as simple as lemonade — you need to decide how many items to produce so that you'll make a profit.

Let's say, for example, that you're selling glasses of lemonade, and you want to make 12 glasses. You know, however, that you'll sell a different number of glasses depending on how you set your price. So, to decide where to set your price, use P as a variable.

### Everyday Examples of Situations to Apply Quadratic Equations | Sciencing

You've estimated the demand for glasses of lemonade to be at 12 - P. Your revenue, therefore, will be the price times the number of glasses sold: Using however much your lemonade costs to produce, you can set this equation equal to that amount and choose a price from there.

Sciencing Video Vault Quadratics in Athletics In athletic events that involve throwing objects like the shot put, balls or javelin, quadratic equations become highly useful. For example, you throw a ball into the air and have your friend catch it, but you want to give her the precise time it will take the ball to arrive.

The graph contains three points and a parabola that goes through all three. The corresponding function is shown in the text box below the graph. If you drag any of the points, then the function and parabola are updated. See the section on manipulating graphs. Answer Return to Contents Standard Form The functions in parts a and b of Exercise 1 are examples of quadratic functions in standard form. If a is positive, the graph opens upward, and if a is negative, then it opens downward.

Any quadratic function can be rewritten in standard form by completing the square. See the section on solving equations algebraically to review completing the square.

### Kids Math: Intro to Linear Equations

The steps that we use in this section for completing the square will look a little different, because our chief goal here is not solving an equation. Note that when a quadratic function is in standard form it is also easy to find its zeros by the square root principle.

Sketch the graph of f and find its zeros and vertex.

Group the x2 and x terms and then complete the square on these terms. When we were solving an equation we simply added 9 to both sides of the equation. In this setting we add and subtract 9 so that we do not change the function.