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### Polynomial Equation (Degree, Leading Coefficient, Constant Term)

Polynomial Equation (Degree, Leading Coefficient, Constant Term)

Polynomial Equation (Degree, Leading Coefficient, Constant Term)

### SOLVED: Which equation represents a quadratic function with a leading coefficient of 2 and a constant term of –3? ^{[1]}

Get 5 free video unlocks on our app with code GOMOBILE. Which equation represents a quadratic function with a leading coefficient of 2 and a constant term of –3?

Which is a quadratic function having a leading coefficient of 3 and a constant term of -12? f(x) = -12x^2 + 3x + 1 f(x) = 3x^2 + 11x – 12 f(x) = 12x^2 + 3x + 3 f(x) = 3x – 12. Which of the following graphs below represents a function of degree 3, where both the sign of the leading coefficient and the constant term in the equation are negative?

Write an equation for a quadratic with the given featuresVertex at $(-3,2),$ and passing through (3,-2). Oops! There was an issue generating an instant solution

### Expert Maths Tutoring in the UK ^{[2]}

Which equations have a leading coefficient of 3 and a constant term of -2? check all that apply.. Given, the leading coefficient and constant term is 3 and -2.

Which equations have a leading coefficient of 3 and a constant term of -2? check all that apply.. The equations having leading coefficient of 3 and constant term of -2 are 0 = 3×2 + 2x – 2, 0 = -3x + 3×2 – 2 and 0 = -1x – 2 + 3×2.

### SOLVED: which is a quadratic function having a leading coefficient of 3 and a constant term of -12 ^{[3]}

Get 5 free video unlocks on our app with code GOMOBILE. which is a quadratic function having a leading coefficient of 3 and a constant term of -12

Find a quadratic function with the given zeros and write it in standard form.$a+1$ and $3 a$, where $a$ is a constant. Write a quadratic function whose zeros are 3 and 12.f(x)

0 f(x) = -2x^2 – x + 3 0 f(x) = 2x^2 + x – 3 0 f(x) = -2x^2 + x + 3 0 f(x) = 2x^2 + x + 3. A quadraticfunction with a vertex at (-1,2) and a y-intercept of 3.

### Polynomial Functions ^{[4]}

– Describe the graphs of basic odd and even polynomial functions. A linear function is a special type of a more general class of functions: polynomials

for some integer [latex]n\ge 0[/latex] and constants [latex]a_n, \, a_{n-1}, \cdots, a_0[/latex], where [latex]a_n\ne 0[/latex].. In the case when [latex]n=0[/latex], we allow for [latex]a_0=0[/latex]; if [latex]a_0=0[/latex], the function [latex]f(x)=0[/latex] is called the zero function

A linear function of the form [latex]f(x)=mx+b[/latex] is a polynomial of degree 1 if [latex]m\ne 0[/latex] and degree 0 if [latex]m=0[/latex]. A polynomial of degree 0 is also called a constant function

### polynomials ^{[5]}

The Improving Mathematics Education in Schools (TIMES) Project. The Improving Mathematics Education in Schools (TIMES) Project

We can factor quadratic expressions, solve quadratic equations and graph quadratic functions, the obvious question arises as to. how these things might be performed with algebraic expressions of higher degree.

Similarly we can factor the cubic x3 − 6×2 + 11x − 6 as (x − 1)(x − 2)(x − 3), which enables us to show that the solutions of x3 − 6×2 + 11x − 6 = 0 are x = 1, x = 2 or x = 3. In this module we will see how to arrive at this factorisation.

### 5.10.3: Key Concepts ^{[6]}

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\). – A polynomial function of degree two is called a quadratic function.

– The axis of symmetry is the vertical line passing through the vertex. The zeros, or intercepts, are the points at which the parabola crosses the axis

– Quadratic functions are often written in general form. Standard or vertex form is useful to easily identify the vertex of a parabola

### Three Techniques for Evaluating and Finding Zeros of Polynomial Functions ^{[7]}

Three Techniques for Evaluating and Finding Zeros of Polynomial Functions. Using the Rational Zero Theorem to Find Rational Zeros

But first we need a pool of rational numbers to test. The Rational Zero Theorem helps us to narrow down the number of possible rational zeros using the ratio of the factors of the constant term and factors of the leading coefficient of the polynomial.

Let us set each factor equal to 0, and then construct the original quadratic function absent its stretching factor.. Notice that two of the factors of the constant term, , are the two numerators from the original rational roots: and

### Business Calculus ^{[8]}

A polynomial is a function that can be written as \[ f(x)=a_0+a_1 x+a_2 x^2+\dots+a_n x^n \]. Each of the \(a_i\) constants are called coefficients and can be positive, negative, or zero, and be whole numbers, decimals, or fractions.

Each individual term is a transformed power function.. The degree of the polynomial is the highest power of the variable that occurs in the polynomial.

The leading coefficient is the coefficient of the leading term.. Because of the definition of the “leading” term we often rearrange polynomials so that the powers are descending: \[ f(x)=a_n x^n+a_{n-1}x^{n-1}\dots a_2 x^2+a_1 x+a_0 \]

### The roots of a quadratic with a mistaken constant term are $-17$ and $15$; with a mistaken leading coefficient, $8$ and $-3$. Find the actual roots. ^{[9]}

Loki and Unloki were independently solving the roots of a quadratic function. Loki got the roots $−17$ and $15$, while Unloki got the roots $8$ and $−3$

What are the actual roots of the quadratic function?. I’ve been thinking about this for a while, but I think I’m missing something.

### Sources

- https://www.numerade.com/ask/question/which-equation-represents-a-quadratic-function-with-a-leading-coefficient-of-2-and-a-constant-term-of-3-24796/#:~:text=For%20example%2C%20if%20we%20choose,a%20constant%20term%20of%20%2D3.
- https://www.cuemath.com/questions/which-equations-have-a-leading-coefficient-of-3-and-a-constant-term-of-2-check-all-that-apply-0-3×2-2x-2/#:~:text=2%20%2B%203×2.-,Which%20equations%20have%20a%20leading%20coefficient%20of%203%20and%20a,1x%20%2D%202%20%2B%203×2.
- https://www.numerade.com/ask/question/which-is-a-quadratic-function-having-a-leading-coefficient-of-3-and-a-constant-term-of-12-20592/#:~:text=Instant%20Answer&text=So%2C%20any%20function%20that%20fits,a%20constant%20term%20of%20%2D12.
- https://courses.lumenlearning.com/calculus1/chapter/polynomial-functions/
- https://www.amsi.org.au/teacher_modules/polynomials.html
- https://math.libretexts.org/Under_Construction/Algebra_and_Trigonometry_2e_(OpenStax)/05%3A_Polynomial_and_Rational_Functions/5.10%3A_Chapter_Review/5.10.03%3A_Key_Concepts
- https://learn.saylor.org/mod/book/tool/print/index.php?id=54129&chapterid=39310
- http://www2.gcc.edu/dept/math/faculty/BancroftED/buscalc/chapter1/section1-6.php
- https://math.stackexchange.com/questions/2974346/the-roots-of-a-quadratic-with-a-mistaken-constant-term-are-17-and-15-with