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# 2.1: Methods for Solving Quadratic Functions

Difficulty Level: At Grade Created by: CK-12
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Practice Methods for Solving Quadratic Functions

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### Vocabulary Language: English

Completing the Square

Completing the square is a common method for rewriting quadratics. It refers to making a perfect square trinomial by adding the square of 1/2 of the coefficient of the $x$ term.

Factor to Solve

"Factor to Solve" is a common method for solving quadratic equations accomplished by factoring a trinomial into two binomials and identifying the values of $x$ that make each binomial equal to zero.

factored form

The factored form of a quadratic function $f(x)$ is $f(x)=a(x-r_{1})(x-r_{2})$, where $r_{1}$ and $r_{2}$ are the roots of the function.

Factoring

Factoring is the process of dividing a number or expression into a product of smaller numbers or expressions.

The quadratic formula states that for any quadratic equation in the form $ax^2+bx+c=0$, $x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$.

A quadratic function is a function that can be written in the form $f(x)=ax^2 + bx + c$, where $a$, $b$, and $c$ are real constants and $a\ne 0$.

Roots

The roots of a function are the values of x that make y equal to zero.

standard form

The standard form of a quadratic function is $f(x)=ax^{2}+bx+c$.

Vertex form

The vertex form of a quadratic function is $y=a(x-h)^2+k$, where $(h, k)$ is the vertex of the parabola.

Zeroes of a Polynomial

The zeroes of a polynomial $f(x)$ are the values of $x$ that cause $f(x)$ to be equal to zero.

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