Find the difference.

Answer:

Step-by-step explanation:

In this lesson, you will learn what the "end behavior" of a polynomial is and how to analyze it from a graph or from a polynomial equation.

What's "end behavior"?

The end behavior of a function

f

ff describes the behavior of the graph of the function at the "ends" of the

x

xx-axis.

In other words, the end behavior of a function describes the trend of the graph if we look to the right end of the

x

xx-axis (as

x

xx approaches

+

∞

+∞plus, infinity) and to the left end of the

x

xx-axis (as

x

xx approaches

−

∞

−∞minus, infinity).

yyxxy=

f(x)

y=f(x)

x gets

more

+ more +

f(x) gets

more

+ more +

For example, consider this graph of the polynomial function

fff. Notice that as you move to the right on the x

xx-axis, the graph of f

ff goes up. This means, as x

xx gets larger and larger,

f(x)

f(x)f, left parenthesis, x, right parenthesis gets larger and larger as well. Mathematically, we write: as

x→+x→+∞x, right arrow, plus, infinity,

f(x)→+∞

f(x)→+∞f, left parenthesis, x, right parenthesis, right arrow, plus, infinity. (Say, "as xxx approaches positive infinity, f(x)

f(x)f, left parenthesis, x, right parenthesis approaches p

5 0

3 years ago

(08.07 HC)

andreev551 [17]

Answer:

$\textsf{A)} \quad x=-2, \:\:x=\dfrac{5}{2}$

$\textsf{B)} \quad \left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)$

C) See attachment.

Step-by-step explanation:

Given function:

$f(x)=2x^2-x-10$

To factor a quadratic in the form $ax^2+bx+c$ , find two numbers that multiply to $ac$ and sum to $b$ :

$\implies ac=2 \cdot -10=-20$

$\implies b=-1$

Therefore, the two numbers are -5 and 4.

Rewrite $b$ as the sum of these two numbers:

$\implies f(x)=2x^2-5x+4x-10$

Factor the first two terms and the last two terms separately:

$\implies f(x)=x(2x-5)+2(2x-5)$

Factor out the common term (2x - 5):

$\implies f(x)=(x+2)(2x-5)$

The x-intercepts are when the curve crosses the x-axis, so when y = 0:

$\implies (x+2)(2x-5)=0$

Therefore:

$\implies (x+2)=0 \implies x=-2$

$\implies (2x-5)=0 \implies x=\dfrac{5}{2}$

So the x-intercepts are:

$x=-2, \:\:x=\dfrac{5}{2}$

The x-value of the vertex is:

$\implies x=\dfrac{-b}{2a}$

Therefore, the x-value of the vertex of the given function is:

$\implies x=\dfrac{-(-1)}{2(2)}=\dfrac{1}{4}$

To find the y-value of the vertex, substitute the found value of x into the function:

$\implies f\left(\dfrac{1}{4}\right)=2\left(\dfrac{1}{4}\right)^2-\left(\dfrac{1}{4}\right)-10=-\dfrac{81}{8}$

Therefore, the vertex of the function is:

$\left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)$

Plot the x-intercepts found in Part A.

Plot the vertex found in Part B.

As the leading coefficient of the function is positive, the parabola will open upwards. This is confirmed as the vertex is a minimum point.

The axis of symmetry is the x-value of the vertex. Draw a line at x = ¹/₄ and use this to ensure the drawing of the parabola is symmetrical.

Draw a upwards opening parabola that has a minimum point at the vertex and that passes through the x-intercepts (see attachment).

5 0

2 years ago

For what value(s) of k is the linear system consistent? (Enter your answers as a comma-separated list.)

AleksAgata [21]

Answer:

Step-by-step explanation:

Given

$6x_1-9x_2=8$

$9x_1+kx_2=-1$

The given system is $AX=B$ can be represented by

$\begin{bmatrix}6 &-9 \\ 9 & k\end{bmatrix}\begin{bmatrix}x_1\\ x_2\end{bmatrix}=\begin{bmatrix}8\\ -1\end{bmatrix}$

The given system is consistent when determinant of A is not equal to zero

$|A|$

$|A|=6k-(-81)=6k+81$

$k\neq \frac{-27}{2}$

i.e. system is consistent for all value of k except $k=\frac{-27}{2}$

$R-\frac{-27}{2}$

4 0

3 years ago

Read 2 more answers

In 2013 Traci joined a swim club. The fees were £600 per year in 2013. Each year the fees increase by 6%. Calculate, to nearest

balandron [24]

Answer:

715 pounds

Step-by-step explanation:

FV = solve

PV = 600

I% = 6

K = 1, N = 3 (2013 - 2016 = 3 years)

Plug it in:

FV = 600 x [ 1 + (6/100 x 1)]³

= 600 x ( 1 + 0.06)³

= 600 x (1.06)³

FV = 714.61, 715 to the nearest dollar.

Therefore, the fee in 2016 is 715 pounds.

6 0

3 years ago

Fiona is trying to prove that a pair of expressions are equivalent by using substitution. Which pair of expressions has the same

fiasKO [112]

Missing Part of the Question

3 (4 - y) -7 ; 5 + 3y

9 + y + 4y - 2 - 3y; -2y + 7

5 + y - 2 - 6y + y; 8y + 3

2y + 7 + y - 2 + y; 4y + 5

Answer:

2y + 7 + y - 2 + y; 4y + 5

Step-by-step explanation:

Given

y = 3

Required

Which pair of expression are equal

To get the pair of expression that are equal; we simply substitute 3 for y in each of the expressions

3 (4 - y) -7 and 5 + 3y

Substitute 3 for y in 3 (4 - y) -7

This gives 3(4 - 3) -7

= 3(1) - 7

= 3 - 7

= -4

Then Substitute 3 for y in 5 + 3y

This gives 5 + 3(3)

= 5 + 9

= 14

-4 and 14 are not equal

---------------------------------------------------------------------------------------

9 + y + 4y - 2 - 3y; -2y + 7

Substitute 3 for y in 9 + y + 4y - 2 - 3y

This gives 9 + 3 + 4(3) - 2 - 3(3)

= 9 + 3 + 12 - 2 - 9

= 13

Then Substitute 3 for y in -2y + 7

This gives -2(3) + 7

= -6 + 7

= 1

13 and 1 are not equal

---------------------------------------------------------------------------------------

5 + y - 2 - 6y + y; 8y + 3

Substitute 3 for y in 5 + y - 2 - 6y + y

This gives 5 + 3 - 2 - 6(3) + 3

= 5 + 3 - 2 - 18 + 3

= -9

Then Substitute 3 for y in 8y + 3

This gives 8(3) + 3

= 24 + 3

= 27

-9 and 27 are not equal

---------------------------------------------------------------------------------------

2y + 7 + y - 2 + y; 4y + 5

Substitute 3 for y in 2y + 7 + y - 2 + y

This gives 2(3) + 7 + 3 - 2 + 3

= 6 + 7 + 3 - 2 + 3

= 17

Then Substitute 3 for y in 4y + 5

This gives 4(3) + 5

= 12 + 5

= 17

17 and 17 are equal

Hence, Option D is correct

6 0

3 years ago