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Chapter 1: Problem 155

What is a quadratic equation?

Short Answer

Expert verified
A quadratic equation is a second-order polynomial equation in the standard form \(ax^2+bx+c=0\), where \(a\), \(b\), and \(c\) are constants. Its graph forms a parabola, and its solutions can be applied in a range of real-life problems.

Step by step solution

01

Definition

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 constants and \(a\) does not equal zero.
02

Details and Real-world Applications

Values of \(x\), for which the equation equals zero, are known as solutions or roots of the equation. Quadratic equations and their solutions appear in diverse real-life situations such as calculation of areas, determination of an object's maximum height in physics, and optimization in operations research.
03

Relationship with Parabolas

Graphically, a quadratic equation describes a parabola, the shape of which depends on the coefficients \(a\), \(b\), and \(c\). When \(a > 0\), the parabola opens upwards like a 'U'. When \(a < 0\), the parabola opens downwards like an 'n'.

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Most popular questions from this chapter

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(\frac{x-4}{6} \geq \frac{x-2}{9}+\frac{5}{18}\)

Solve absolute value inequality. \(|x+3| \leq 4\)

Solve compound inequality. \(-3 \leq \frac{2}{3} x-5<-1\)

Use interval notation to express solution sets and graph each solution set on a number line. Solve linear inequality. \(5(x-2)-3(x+4) \geq 2 x-20\)

Solve absolute value inequality. \(1<\left|x-\frac{11}{3}\right|+\frac{7}{3}\)
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