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3 years ago

use what you know about zeros of a function and end behavior of a graph that matches the function f(x) = (x+3)(x+2)(x-1)

Mathematics

1 answer:

Gwar [14]3 years ago

3 0

Answer:

The zeros are x=-3,-2,1

end behavior is one up one down

Step-by-step explanation:

The zeros are x=-3,-2,1

The end behaviors are one up one down because the function is of degree 3 meaning it is odd function and has opposite end directions.

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1) Determine the discriminant of the 2nd degree equation below:

Aleksandr-060686 [28]

$\LARGE{ \boxed{ \mathbb{ \color{purple}{SOLUTION:}}}}$

We have, Discriminant formula for finding roots:

$\large{ \boxed{ \rm{x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} }}}$

Here,

x is the root of the equation.
a is the coefficient of x^2
b is the coefficient of x
c is the constant term

1) Given,

3x^2 - 2x - 1

Finding the discriminant,

➝ D = b^2 - 4ac

➝ D = (-2)^2 - 4 × 3 × (-1)

➝ D = 4 - (-12)

➝ D = 4 + 12

➝ D = 16

2) Solving by using Bhaskar formula,

❒ p(x) = x^2 + 5x + 6 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5\pm \sqrt{( - 5) {}^{2} - 4 \times 1 \times 6 }} {2 \times 1}}}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5 \pm \sqrt{25 - 24} }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5 \pm 1}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = - 2 \: or - 3}}}$

❒ p(x) = x^2 + 2x + 1 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm \sqrt{ {2}^{2} - 4 \times 1 \times 1} }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm \sqrt{4 - 4} }{2} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm 0}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = - 1 \: or \: - 1}}}$

❒ p(x) = x^2 - x - 20 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - ( - 1) \pm \sqrt{( - 1) {}^{2} - 4 \times 1 \times ( - 20) } }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ 1 \pm \sqrt{1 + 80} }{2} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{1 \pm 9}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = 5 \: or \: - 4}}}$

❒ p(x) = x^2 - 3x - 4 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - ( - 3) \pm \sqrt{( - 3) {}^{2} - 4 \times 1 \times ( - 4) } }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{3 \pm \sqrt{9 + 16} }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{3 \pm 5}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = 4 \: or \: - 1}}}$

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5 0

3 years ago

Read 2 more answers

)A poster is shown below 3ft and 12 ft

iren2701 [21]

The answer your looking for is 7.5ft by 1.5ft hope this helped have a nice day :)

6 0

4 years ago

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Samantha visits for local farmers market to buy apples and oranges to make a fruit salad. she has $10 to spend. Apples are $.26.

GrogVix [38]

She can buy 38 apples.

10/0.26 = 38.5 but you can’t buy half an apple so you round down to 38.

Hope this helped!

5 0

3 years ago

Read 2 more answers

Iris wants to buy sneakers at $15 each and high heels at $30 each. Write an algebraic expression to find the total cost of the s

kogti [31]

Answer: 30y + 15x

If x is for sneakers, and y is for high heels, plug 15 in for a and 30 in for b. This means that x is how many sneakers she buys, and y is how many high heels she buys. The equation altogether represents the total amount of her purchases.

5 0

3 years ago

Boris choos three diffrent numbers.the sum of the three numbers is 36.One of trh numbers is a cube number.the other two number a

inna [77]

Answer:

4,5,27

Problem:

Boris chose three different numbers.

The sum of the three numbers is 36.

One of the numbers is a perfect cube.

The other two numbers are factors of 20.

Step-by-step explanation:

Let's pretend those numbers are:

$a,b, \text{ and } c$ .

We are given the sum is 36: $a+b+c=36$ .

One of our numbers is a perfect cube. $a=n^3$ where $n$ is an integer.

The other two numbers are factors of 20. $bk=20$ and $ci=20$ where $a,c,i, \text{ and } k \text{ are integers}$ .

$n^3+\frac{20}{k}+\frac{20}{i}=36$

From here I would just try to find numbers that satisfy the conditions using trial and error.

$3^3+\frac{20}{2}+\frac{20}{2}$

$27+10+10$

$47$

$3^3+\frac{20}{4}+\frac{20}{5}$

$27+5+4$

$36$

So I have found a triple that works:

$27,5,4$

The numbers in ascending order is:

$4,5,27$

4 0

3 years ago

use what you know about zeros of a function and end behavior of a graph that matches the function f(x) = (x+3)(x+2)(x-1)​

use what you know about zeros of a function and end behavior of a graph that matches the function f(x) = (x+3)(x+2)(x-1)