What describes the reflection of the figure?

Do you agree with the statement that " cubic functions must have at least 1 x-intercept but not more than 3, whereas quadratic f

vladimir2022 [97]

Answer:

Yes, I agree

Step-by-step explanation:

For the cubic function

A cubic function is represented as:

$f(x)=ax^3+bx^2+cx+d$

A cubic function may have 1, 2 or 3 x intercepts. This is shown below

For 3 x intercepts

$y = x^3 - x$

Equate y to 0

$x^3 - x = 0$

Expand

$x(x^2 - 1) = 0$

Express $x^2 - 1$ as difference of two squares

$x(x - 1)(x +1 ) = 0$

x = 0 or 1 or -1

For 2 x intercepts

$y = x^3 - x$

$y =(x-5)^2)(x+7)$

Equate y to 0

$(x-5)^2(x+7) = 0$

Expand

$(x-5)(x-5)(x+7) = 0$

x= 5 or x = -7

For 1 x intercept

$y = x^3$

Equate y to 0

$x^3 = 0$

Take cube roots of both sides

$x = 0$

It has been shown above that a cubic function may have 1, 2 or 3.

So, I agree to the statement

For the quadratic function

A quadratic function will not have any x intercept when the function can not be factorized;

E.g.

$y = x^2 + x + 17$

The above function has no x intercept.

A quadratic function will have at least 1 x intercept when the function can be factorized;

E.g.

$y = x^2- 6x + 9$

Equate y to 0

$x^2- 6x + 9 = 0$

Expand

$x^2 - 3x - 3x + 9 = 0$

$(x - 3)(x-3) = 0$

$x = 3$

We've shown that a quadratic may have no x intercept, and it may also have x intercept(s)

Hence, I agree to both statement

3 0

2 years ago

THESE FRKN TEACHERS MAKE NO SENSE THEIR CLUELESS SOMEONE HELP AND JUST WRITE THE ANSWER ILL BRAINLLIST

SashulF [63]

Answer:

Whats F five is that a point or something???

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

I NEED HELP PLEASE Which is the better buy?

Vladimir79 [104]

Answer: The second one, 10 rolls for $12. 1.29 (Rounded)

Step-by-step explanation:

14/18 is 1.29 (Rounded)

10/12 is 1.20.

The unit rate is cheaper, therefore making it the better buy

6 0

2 years ago

Read 2 more answers

When it is easier to use the point-slope form to write the equation of a line and when it is easier to use the slope-intercept f

Pani-rosa [81]

Point slope form is used when we have the information of at least two coordinates that lie on the line

For example:

Given that coordinate (3, 4) and (6, 7) lies on a straight line.

We work out the equation of the line by substituting the two coordinates into the formula (y - y₁) = m(x - x₁) where (x₁, y₁) could be either (3, 4) and (6, 7).

We would need to use both coordinates to work out the gradient (m) by using the formula:
$m= \frac{vertical distance}{horizontal distance} = \frac{y_2-y_1}{x_2-x_1}$
----------------------------------------------------------------------------------------------------------------

The slope intercept form is used when we are given enough information to work out the gradient as well as the y-intercept.

For example:
Given two coordinates (3, 5) and (0, 9)
This information can help to find the gradient and the y-intercept.
The y-intercept would be at 9 because the (0, 9)
We calculate the gradient m
Then substitute into y=mx+c which is the slope intercept form.

3 0

3 years ago

A whale is at the surface of the ocean tto breathe. What is the whale's elevation? Draw a numhber line

ratelena [41]

Answer:0

<—————|—————>
0

Step-by-step explanation:

4 0

2 years ago