14 plus 5(x plus 3) minus 7

Which is an equation of the parabola that intersects the x-axis at points (-1, 0) and (3, 0)? Show your work or explain how you

hichkok12 [17]

Answer:

$\displaystyle \large{y=x^2-2x-3}$

Step-by-step explanation:

The given points are (-1,0) and (3,0) to find an equation of parabola. Notice that they say or the given points are x-intercepts, which means they make it easier for us to find an equation of parabola using these x-intercepts.

Quick Note:

x-intercepts are simply the roots or solutions of quadratic equation, so if our root is x = -2 then we can write as (-2,0) and write back to x+2=0.

So what we are going to do is to write the roots’ equation back as $\displaystyle \large{x+\alpha =0}$

Our points or roots are given, therefore:

If x = -1 then x+1=0

If x = 3 then x-3=0

Then multiply x+1 with x-3 because if (x-1)(x+3)=0 then x-1=0 or x+3=0:

$\displaystyle \large{(x+1)(x-3)=0}$

Convert 0 to y since we want to find a function:

$\displaystyle \large{(x+1)(x-3)=y}\\\displaystyle \large{y=(x+1)(x-3)}$

Expand the expressions in and simplify to standard form:

$\displaystyle \large{y=x^2-3x+x-3}\\\displaystyle \large{y=x^2-2x-3}$

Therefore, the equation is $\displaystyle \large{y=x^2-2x-3}$

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Summary

If we are given the points $\displaystyle \large{(\alpha ,0)}$ and $\displaystyle \large{(\beta ,0)}$ with wideness of the graph or a-value = 1 then the parabola equation is:

$\displaystyle \large{y=(x-\alpha )(x-\beta )}\\\displaystyle \large{y=x^2-\beta x-\alpha x+\alpha \beta }\\\displaystyle \large{y=x^2-(\beta +\alpha )x+\alpha \beta }$

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Others

If you have any doubts about my answer, explanation or this question, do not hesitate to let me know in the comment!

3 0

3 years ago

A presidential candidate plans to begin her campaign by visiting the capitals in 4 of 42 states. What is the probability that sh

marissa [1.9K]

Answer:

P (She selects the route of four specific capitals) = $\frac{1}{2686320}=(3.7226)10^{-7}$

D. No,it is not practical to list all of the different possible routes because the number of possible permutations is very large.

Step-by-step explanation:

Let's start assuming that each route is equally likely to be chosen.

Assuming this, we can calculate P(A) where the event A is ''She selects the route of four specific capitals'' doing the following :

P(A) = Favourable cases in which the route of four specific capitals is selected / Total number of ways in 4 of 42 states

The favourable cases in which the route of four specific capitals is selected is equal to 1 .

For the denominator we need the permutation number of 4 in 42.

The permutation number is defined as :

$nPr=\frac{n!}{(n-r)!}$

$42P4=\frac{42!}{(42-4)!}=\frac{42!}{38!}=2686320$

The probability of event A is : $\frac{1}{2686320}=(3.7226)10^{-7}$

Finally for the other question : The option D is the correct because the number of possible permutations is 2686320 and is very large to be listed.

7 0

3 years ago

A square has a perimeter of 12x 52 units. which expression represents the side length of the square in units? x 4 x 40 3x 13 3x

d1i1m1o1n [39]

The expression which represents the side length of the square which has perimeter of 12x 52 units is 3x+12 units.

<h3>What is the perimeter of a square?</h3>

The measure of the boundary of the sides of a square is called its perimeter. The perimeter of a square is 4 times the side of the square.

$P=4a$

Here, (<em>a</em>) is the side of the square.

A square has a perimeter of 12x +52 units. The perimeter of a square is 4 times the side of the square. Thus, the side of this square is,

$P=4a\\12x +52=4a\\a=\dfrac{12x +52}{4}\\a=\dfrac{4(3x +12)}{4}\\a=3x+12$

Thus, the expression which represents the side length of the square which has perimeter of 12x 52 units is 3x+12 units.

Learn more about the perimeter of the square here;

brainly.com/question/25092270

7 0

2 years ago

Which is bigger 200 mm or 1m

UNO [17]

! meter is greater than 200 milimeters

4 0

4 years ago

Read 2 more answers

The rate for one unit of a given quantity is called a(n)

asambeis [7]

<span>The rate for one unit of a given quantity is called a u</span>nit rate.

6 0

4 years ago