All categories

3 years ago

James creates the table shown to represent the function ƒ(x) = x2 + 8x + 12. Determine the zero(s) of the function.

2 answers:

8 0

I believe that the zeros would be -2 and -6, assuming that the first 2 that you wrote in the equation is supposed to be a power to the x.

skad [1K]3 years ago

8 0

Answer:

x = -6 and -2 are the zero(s) of the function

Step-by-step explanation:

To find the zero(s) of the function f(x).

Given the function:

$f(x) = x^2+8x+12$

Set f(x) = 0

then;

$x^2+8x+12 = 0$

Now factorize the equation as:

$x^2+6x+2x+12 = 0$

⇒ $x(x+6)+2(x+6) = 0$

take (x+6) common we have;

$(x+6)(x+2)=0$

By zero product property we have;

⇒x+6 = 0 or x+2 = 0

⇒x = -6 or x = -2

therefore, the zero(s) of the function are -6 and -2

You might be interested in

Benny brought five new baseball trading cards to add to his collection. the next day his dog ate half of his collection. there a

VMariaS [17]

Benny started with 55 five cards. In order for his dog to have eaten half his cards and end up with 30 cards, that would mean he had 60 cards. Mind you, he had bought 5 more the day before his dog ate them. I hope that makes sense

7 0

2 years ago

Read 2 more answers

Use complete sentences to describe why √-1 ≠ -√1

tekilochka [14]

Well let's say that to compare these two numbers, we have to start with the definition first.

Definition

$\displaystyle \large{ {y}^{2} = x} \\ \displaystyle \large{ y = \pm \sqrt{x} }$

Looks like we can use any x-values right? Nope.

The value of x only applies to any positive real numbers for one reason.

As we know, any numbers time itself will result in positive. No matter the negative or positive.

Definition II

$\displaystyle \large{ {a}^{2} = a \times a = |b| }$

Where b is the result from a×a. Let's see an example.

Examples

$\displaystyle \large{ {2}^{2} = 2 \times 2 = 4} \\ \displaystyle \large{ {( - 2)}^{2} = ( - 2) \times ( - 2) = | - 4| = 4}$

So basically, their counterpart or opposite still gives same value.

Then you may have a question, where does √-1 come from?

It comes from this equation:

$\displaystyle \large{ {y}^{2} = - 1}$

When we solve the quadratic equation in this like form, we square both sides to get rid of the square.

$\displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{ - 1} }$

Then where does plus-minus come from? It comes from one of Absolute Value propety.

Absolute Value Property I

$\displaystyle \large{ \sqrt{ {x}^{2} } = |x| }$

Solving absolute value always gives the plus-minus. Therefore...

$\displaystyle \large{ y = \pm \sqrt{ - 1} }$

Then we have the square root of -1 in negative and positive. But something is not right.

As I said, any numbers time itself of numbers squared will only result in positive. So how does the equation of y^2 = -1 make sense? Simple, it doesn't.

Because why would any numbers squared result in negative? Therefore, √-1 does not exist in a real number system.

Then we have another number which is -√1. This one is simple.

It is one of the solution from the equation y^2 = 1.

$\displaystyle \large{ {y}^{2} = 1} \\ \displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{1} } \\ \displaystyle \large{ y = \pm \sqrt{1} }$

We ignore the +√1 but focus on -√1 instead. Of course, we know that numbers squared itself will result in positive. Since 1 is positive then we can say that these solutions exist in real number.

Conclusion

So what is the different? The different between two numbers is that √-1 does not exist in a real number system since any squared numbers only result in positive while -√1 is one of the solution from y^2 = 1 and exists in a real number system.

5 0

3 years ago

Read 2 more answers

2-9*7+5=

Fed [463]

7*7=49+5=54 just use PEMDAS

7 0

3 years ago

Read 2 more answers

In a small library , there are 5 nonfiction books for every 9 fiction books There are 130 a . How many fiction books are there ?

Mice21 [21]

Answer: 234