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Chapter 3: Problem 74

What is a quadratic function?

Short Answer

Expert verified
A quadratic function is a polynomial function of the second degree, represented as \(y = ax^2 + bx + c\), where \(a\), \(b\), and \(c\) are constants and \(x\) is the variable. It forms a curve called a parabola. The shape, direction, and position of the parabola depend on the values of \(a\), \(b\), and \(c\).

Step by step solution

01

Definition of a Quadratic Function

A quadratic function is a polynomial function of the second degree. In general form, it's represented as \(y = ax^2 + bx + c\), where \(a\), \(b\), and \(c\) are constants and \(x\) is the variable.
02

Explanation of the Formula

In the equation \(y = ax^2 + bx + c\): \n- \(a\) is the coefficient of \(x^2\) and it determines the direction and the width of the parabola. If \(a > 0\), the parabola opens upward, if \(a < 0\), the parabola opens downward.\n- \(b\) is the coefficient of \(x\), and it affects the direction and the position of the parabola along the x-axis. \n- \(c\) is the constant term, it's where the graph of the quadratic function crosses the y-axis, it's the y-intercept.
03

Graphical representation

A quadratic function forms a curve called a parabola. Parabolas can open upwards, or downwards, and vary in 'width' or 'steepness', but they all have the same basic 'U' shape.

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Most popular questions from this chapter

Write an equation that expresses each relationship. Then solve the equation for \(y .\) \(x\) varies jointly as \(z\) and the sum of \(y\) and \(w\).

Use the four-step procedure for solving variation problems given on page 424 to solve. \(y\) varies directly as \(x\) and inversely as the square of \(z . y=20\) when \(x=50\) and \(z=5 .\) Find \(y\) when \(x=3\) and \(z=6\).

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