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Chapter 6: Problem 88

What is a quadratic equation?

Short Answer

Expert verified
A quadratic equation is a second-order polynomial equation in a single variable \(x\), with a nonzero coefficient for \(x^2\). It is typically represented in this standard form: \(ax^2 + bx + c = 0\).

Step by step solution

01

Definition of Quadratic Equation

A quadratic equation is a second-order polynomial equation that can be expressed in the standard form \(ax^2 + bx + c = 0\), where \(a\), \(b\), and \(c\) are coefficients, \(a 鈮� 0\), and \(x\) represents an unknown variable.
02

Identifying the Quadratic Equation

The equation should hold the form stated above and it's recognized by the highest exponent being 2. That's why it's a 'quadratic', which comes from 'quad' meaning square 鈥� as in \(x^2\).
03

Understanding Coefficients

In the equation, three numbers define its structure - \(a\), \(b\), and \(c\). These are coefficients that, when varied, will change the parabolic shape of the graph that represents the quadratic equation.

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Most popular questions from this chapter

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$4 a y^{3}-12 a y^{2}+9 a y$$

Describe a strategy that can be used to factor polynomials.

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$27 x^{2}+75$$

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$9 y^{2}+64$$

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$15 a^{2}+11 a b-14 b^{2}$$
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