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Boundless Algebra
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Chapter 6

Quadratic Functions and Factoring

Book Version 13
By Boundless
Boundless Algebra
Algebra
by Boundless
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Section 1
Introduction to Quadratic Functions
What is a Quadratic Function?

Quadratic equations are second order polynomials, and have the form $f(x)=ax^2+bx+c$.

The Quadratic Formula

The zeros of a quadratic equation can be found by solving what is known as the quadratic formula.

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The Discriminant

The discriminant of a polynomial is a function of its coefficients that reveals information about the polynomial's roots.

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Other Equations in Quadratic Form

Many equations with no odd-degree terms can be reduced to quadratics and solved with the same methods as quadratics.

Section 2
Graphs of Quadratic Functions
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Parts of a Parabola

The graph of a quadratic function is a parabola, and its parts provide valuable information about the function.

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A Graphical Interpretation of Quadratic Solutions

The roots of a quadratic function can be found algebraically or graphically.

Graphing Quadratic Equations in Vertex Form

The graph of a quadratic function is a parabola whose axis of symmetry is parallel to the $y$-axis.

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Graphing Quadratic Equations In Standard Form

A quadratic function is a polynomial function of the form $y=ax^2+bx+c$.

Section 3
Factoring
Solving Quadratic Equations by Factoring

A quadratic equation of the form $ax^2+bx+c=0$ can sometimes be solved by factoring the quadratic expression.

Factoring Perfect Square Trinomials

When a trinomial is a perfect square, it can be factored into two equal binomials.

Factoring a Difference of Squares

When a quadratic is a difference of squares, there is a helpful formula for factoring it.

Factoring General Quadratics

Polynomials of the form $ax^2+bx+c$ can be factored via the trial and error method.

Completing the Square

Completing the square is a common method for solving quadratic equations, and takes the form of $0=a(x-h)^2 + k$.

Section 4
Applications of Quadratic Functions
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Scientific Applications of Quadratic Functions

Quadratic relationships between variables are commonly found in physical sciences, engineering, and elsewhere.

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Financial Applications of Quadratic Functions

For problems involving quadratics in finance, it is useful to graph the equation. From these, one can easily find critical values of the function by inspection.

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Boundless Algebra by Boundless
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Quadratic Functions and Factoring
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Polynomials and Rational Functions
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