Mathematics: Select the graph of the quadratic function. f(x)=-6x^2

Select the graph of the quadratic function. f(x)=-6x^2

Ответ:

natalieagustinlop54

23.10.2022

The required polynomial function is $\bf f\left(x\right) =\left( {x+5}\right)\left({x+5}\right)\left({x+5}\right)\left({x+4}\right)\left({x - 2}\right)\left( {x-9}\right)$ .

Further explanation:

From the given problem, it is observed that for the required function f(x) there are 6 roots which are -4,2,9,-5,-5 and . It is possible only for the functions $f\left(x\right)=\left({x+5}\right)\left( {x+5}\right)\left({x+5}\right)\left( {x+4}\right)\left( {x -2}\right)\left({x -9}\right)$ or $f\left(x\right)=\left({x-5}\right)\left( {x-5}\right)\left({x-5}\right)\left({x-4}\right)\left({x + 2}\right)\left( {x+9}\right)$ .

Since, the coefficients of all for both the function is 1, the leading coefficient of both the function is 1.

The roots of the polynomial function $f\left(x\right)=\left({x+5}\right)\left({x+5}\right)\left({x+5}\right)\left({x+4}\right)\left({x -2} \right)\left({x-9}\right)$ is obtained as follows:

$\left({x+5}\right)\left({x+5}\right)\left({x+5}\right)\left({x+4}\right)\left({x-2} \right)\left( {x -9}\right) = 0$

Solution 1:

$\begin{aligned}\left( {x+5}\right)\left({x+5}\right)\left({x+5}\right)&= 0\hfill\\ x &=-5\,\,\,\,\,\,\,\,\,\,\left( {{\text{with multiplicity 3}}}\right)\hfill\\\end{aligned}$

Solution 2:

$\begin{aligned}\left({x+4}\right)&=0\hfill\\x&=-4\,\,\,\,\,\,\,\,\,\,\left( {{\text{with multiplicity 1}}} \right)\hfill\\ \end{gathered}$

Solution 3:

$\begin{aligned}\left( {x-2} \right)&=0\hfill \\ x&=2\,\,\,\,\,\,\,\,\,\,\left( {{\text{with multiplicity 1}}}\right)\hfill\\ \end{aligned}$

Solution 4:

$\begin{aligned}\left({x - 9} \right)&=0\hfill\\x&=9\,\,\,\,\,\,\,\,\,\,\left( {{\text{with multiplicity 1}}}\right)\hfill\\ \end{aligned}$

Therefore, the zeros of the polynomial function $f\left(x\right)=\left({x+5}\right)\left({x+5}\right)\left({x+5}\right)\left({x+4}\right)\left( {x -2}\right)\left({x-9}\right)$ are -4,2,9,-5,-5 and .

Thus, the required polynomial function is $\bf f\left(x\right) =\left( {x+5}\right)\left({x+5}\right)\left({x+5}\right)\left({x+4}\right)\left({x - 2}\right)\left( {x-9}\right)$ .

Learn more:

1. Which function has an inverse that is also a function? {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}

2. A given line has the equation 10x + 2y = −2. what is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)? y = ( )x + 12

3. what are the domain and range of the function f(x) = 3x + 5?

Answer Details :

Grade: High School.

Subject: Mathematics.

Chapter: linear equation.

Keywords:

Polynomial function, root, zeroes, solution, multiplicity, f(x)=(x+5)(x+5), linear equation, quadratic, cubic expression, linear equation, zeros, function, substitution, origin, shaded, region, solution of inequality graph.

0,0(0 оценок)

Select the graph of the quadratic function. f(x)=-6x^2

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question