Mathematics, 01.12.2020 07:40 prinxcess1206

Consider the function f(x) = x2 + 2x – 15. What are the x-intercepts of the function?

Answers: 1

Show answers

Answers

Answer from: mistyshaw3736

The x-intercepts of the function are x = 3 and x = -5 .

Step-by-step explanation:

We are given the function $\displaystyle f(x) = x^2 + 2x - 15$ .

In order to find the x-intercepts of the equation, we need to solve this quadratic. We can use factoring methods to solve it.

The parent function for a quadratic is f(x) = ax^2 + bx + c = 0 .

We can use this information to determine what factoring technique we want to use.

There are several different methods, including using the quadratic formula, but because this is easily factorable, we can avoid using it.

We see that our a is equal to 1 (there is no coefficient in front of x²), so we can use the easier of the techniques:

Find what factors of c add up to give you b.Add to x if positive or subtract from x if negative and set it equal to zero.Solve for x - these are your x-intercepts.

Therefore, let's determine what our c is: 15.

Now, let's label the factors for 15.

15 cannot be divided by 2 evenly.15 can be divided by 3 evenly: 15/3 = 515 cannot be divided by 4 evenly.15 can be divided by 5 evenly: 15/5 = 3

Therefore, our two factors are 3 and 5 since they cannot be broken down any further (they are prime numbers - we just performed prime factorization).

Now, we need to pay attention to the sign for c. It's negative, so one of our factors needs to be negative. Therefore, we can test this out:

Now, we check for which one matches the sign for b. This is positive 2, so our two factors are 5 and -3.

Finally, to factor, we add or subtract the factors from x depending on the sign. If the factor is positive, we add it. If the factor is negative, we subtract it. Therefore, we can set up our equations.

$x + 5 = 0\\\\x = -5$

$x - 3 = 0\\\\x = 3$

Therefore, for when x = 3 or x = -5, the line crosses the x-axis. These are the x-intercepts of the function.

Our answers are x = -5 and x = 3.

Answer from: Quest

the length of o'p' is $1.5\times op$ .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

$k=\frac{o'p'}{op}$

the scale factor is 1.5.

$1.5=\frac{o'p'}{op}$

multiply both sides by op.

$1.5\times op=o'p'$

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is $1.5\times op$ .

Answer from: Quest

answer: 0.26

i used the calculator on google

Another question on Mathematics

Mathematics, 21.06.2019 21:30

Ahypothesis is: a the average squared deviations about the mean of a distribution of values b) an empirically testable statement that is an unproven supposition developed in order to explain phenomena a statement that asserts the status quo; that is, any change from what has been c) thought to be true is due to random sampling order da statement that is the opposite of the null hypothesis e) the error made by rejecting the null hypothesis when it is true

Answers: 2

Answer

Mathematics, 21.06.2019 21:30

Select all the statements that apply to this figure

Answers: 2

Answer

Mathematics, 22.06.2019 00:00

Aclothing designer is selecting models to walk the runway for her fashion show. the clothes she designed require each model’s height to be no more than y inches from 5 feet 10 inches, or 70 inches. which graph could be used to determine the possible variance levels that would result in an acceptable height, x?

Answers: 2

Answer

Mathematics, 22.06.2019 01:00