# Problem Solving With Quadratic Equations But the Quadratic Formula took longer and provided me with more opportunities to make mistakes.Warning: Don't get stuck in the rut of always using the Quadratic Formula!

As such, companies often make vector images of their logos, in which the information is stored as mathematical formulae.

Such vector images are easily scaled while maintaining sharp, crisp images.

We cannot take the square root of a negative number.

So, when we substitute , , and into the Quadratic Formula, if the quantity inside the radical is negative, the quadratic equation has no real solution. The quadratic equations we have solved so far in this section were all written in standard form, .

We will see in the next example how using the Quadratic Formula to solve an equation with a perfect square also gives just one solution.

When we solved the quadratic equations in the previous examples, sometimes we got two solutions, sometimes one solution, sometimes no real solutions.Since I'll be cutting equal-sized squares out of all of the corners, and since the box will have a square bottom, I know I'll be starting with a square piece of cardboard.In this last exercise above, you should notice that each solution method gave the same final answer for the cardboard's width.Is there a way to predict the number of solutions to a quadratic equation without actually solving the equation?Yes, the quantity inside the radical of the Quadratic Formula makes it easy for us to determine the number of solutions.Now, we will go through the steps of completing the square in general to solve a quadratic equation for .It may be helpful to look at one of the examples at the end of the last section where we solved an equation of the form as you read through the algebraic steps below, so you see them with numbers as well as ‘in general.’ This last equation is the Quadratic Formula.That can happen, too, when using the Quadratic Formula.If we get a radical as a solution, the final answer must have the radical in its simplified form.Take the extra half a second to find the right answer the right way.sorts of word problems, it is usually helpful to draw a picture.

## Comments Problem Solving With Quadratic Equations

• ###### General Quadratic Word Problems - Purplemath Home
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Most quadratic word problems should seem very familiar, as they are built from the linear problems that you've done in the past. A picture has a height that is 4/3 its width. It is to be enlarged to have an area of 192 square inches. What will be the dimensions of the enlargement?…

• ###### Real World Examples of Quadratic Equations - Math is Fun
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Quadratic Equations are useful in many other areas For a parabolic mirror, a reflecting telescope or a satellite dish, the shape is defined by a quadratic equation. Quadratic equations are also needed when studying lenses and curved mirrors. And many questions involving time, distance and speed need quadratic equations.…

• ###### Quadratic Equations - Problems 1
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Quadratic Functions Problems with Solutions Parabola Questions and Problems with Detailed Solutions Solve Quadratic Equations Using Discriminants Solve Equations, Systems of Equations and Inequalities.…

• ###### Ways to Solve Quadratic Equations - wikiHow
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A quadratic equation is a polynomial equation in a single variable where the highest exponent of the variable is 2. There are three main ways to solve quadratic equations 1 to factor the quadratic equation if you can do so, 2 to use the quadratic formula, or 3 to complete the square.…

• ###### Solving quadratic equations by factoring examples
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Here we are going to see some example problems on solving quadratic equations using the method factoring. Solving quadratic equations by factoring in the form ax ² + bx + c. Whenever we have a quadratic equation in the form ax ² + bx + c and we need to factor this, first we have to check whether the coefficient of x ² is 1 or not.…

• ###### Algebra - Quadratic Equations - Part I Practice Problems
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Here is a set of practice problems to accompany the Quadratic Equations - Part I section of the Solving Equations and Inequalities chapter of the notes for Paul Dawkins Algebra course at Lamar University.…

• ###### Solve quadratic equations with the quadratic formula.
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Solve quadratic equations using the quadratic formula. For example, solve -9x+10x²+8=14. If you're seeing this message, it means we're having trouble loading.…

• ###### Word problems involving quadratic Equations with solutions.
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In order to learn how to solve quadratic equations by four different methods, please follow this tutorial. This tutorial assumes that you have already got a good skill in solving quadratic equations as explained in the above tutorial. This tutorial primarily focuses on solving real-world problems involving quadratic equations. E.g.1…