HELP PLEASE!!!
Identify a point and two x intercepts to write the x-intercept form equation of each parabola.
Answers
x intercepts are 5 and 7
The third point I used was (6,-2); however, you can use any other point you want as long as it's not one of the x intercepts mentioned.
==========================================================
Explanation:
The x intercepts are 5 and 7, where the parabola crosses the x axis. Because of these roots, the two factors are x-5 and x-7.
We can think of the root x = 5 turning into x-5 = 0 after subtracting 5 from both sides. The same goes for x = 7 turning into x-7 = 0.
Put together, the two factors lead to (x-5)(x-7) and we get the equation y = (x-5)(x-7). Plugging either x = 5 or x = 7 into this equation produces y = 0.
-------------------
Notice that plugging in x = 6 leads to...
y = (x-5)(x-7)
y = (6-5)(6-7)
y = (1)(-1)
y = -1
However, the graph shows that x = 6 should lead to y = -2 instead. To fix this, we can stick a 2 out front like so
y = 2(x-5)(x-7)
y = 2(6-5)(6-7)
y = 2(1)(-1)
y = -2
The error has been fixed. As you can see, we need this third point to help nail down the parabolic equation. You can pick any other x value you want as long as it's not 5 or 7.
-------------------
Let's try another x value. Let's say we pick x = 8
y = 2(x-5)(x-7)
y = 2(8-5)(8-7)
y = 2(3)(1)
y = 6
We see that x = 8 leads to y = 6. This matches what the graph shows that (8,6) is a point on the parabola. I'll let you try other x values.
-------------------
In short, we used the roots 5 and 7 to generate the partial factorization (x-5)(x-7). Then we used a third point (6,-2) to help determine the coefficient out front which was 2.
So after using that point, we go from y = (x-5)(x-7) to y = 2(x-5)(x-7) which is the final answer. This is considered x-intercept form because we can quickly read off the x intercepts from this equation.
Related Questions
The best way to accurately solve real-life problems involving decimals is through/by?
Answers
Answer:
Rounding maybe
Step-by-step explanation:
Noah has 3 meters of rope. How many 3/4 meter pieces of rope can he cut from it?
Answers
Answer:
4
Step-by-step explanation:
3/(3/4)=4
Which ordered pairs are on the line with the equation y+3.5=0.75(x−2)? Select each correct answer. A. (4, −2) B. (1, 1.75) C. (7, 5.5) D. (−4, −8)
Answers
Answer:
A
Step-by-step explanation:
Answer: 4, -2
Step-by-step explanation: I just visualized the graph in my head and went from there
find vertex and min/max !! HELP ASAP!!
y=-2(x+9)(x+3)
Answers
Answer:
max at (- 6, 18 )
Step-by-step explanation:
Given the equation of a parabola in intercept form
y = a(x + c)(x + d)
• If a > 0 then min vertex
• If a < 0 then max vertex
y = - 2(x + 9)(x + 3) ← is in intercept form
with a = - 2 < 0 then max vertex
y = - 2(x + 9)(x + 3) ← expand factors using FOIL
= - 2(x² + 12x + 27) ← distribute parenthesis by - 2
y = - 2x² - 24x - 54 ← in standard form
with a = - 2 and b = - 24
The x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex] = - [tex]\frac{-24}{-4}[/tex] = - 6
Substitute x = - 6 into the equation and evaluate for y
y = - 2(- 6 + 9)(- 6 + 3) = - 2(3)(- 3) = 18
vertex = (- 6, 18 ) and is a max
PLEASE HELP WILL MARK BRAINLIEST
Answers
Answer:
a
Step-by-step explanation:
triangles one and two are both isosceles meaning they each have two equal sides they each have a 30-degree angle explain why these triangles do not have to be similar to each other
Answers
Answer:
See below for answers
Step-by-step explanation:
These triangle do not have to be similar to each other because the 30° angles may not be located in the same place.
For example, place one 30° at the vertex of the triangle which is located where the two equal legs of the isosceles triangle are joined. The triangle angles measure are 30°, 75°, and 75°.
But if the 30° angle is one angle at the base of the isosceles triangle, then the angles measure are 30°, 30°, 120°.
30°
Δ Δ
30°
Help please I really don’t understand due in 3 days
Answers
Answer:
x < 4
Step-by-step explanation:
3x - 3 < 9 ( add 3 to both sides )
3x < 12 ( divide both sides by 3 )
x < 4
Answer:
x < 4.
Step-by-step explanation:
3x - 3 < 9
Add 3 to both sides:
3x < 9 + 3
3x < 12
Divide both sides by 3:
x < 4.
140 grams of almonds cost $3.5. Mechael needs almonds for the dish she is preparing. How much she has to pay for 500 grams of almonds cost?
Answers
Answer:
$12.5
Step-by-step explanation:
140 divided by 7 is 20, since 20 is a factor of 500, it will make it easier. Since we divided the 140 grams by 7, we also have to divide the $3.5 by 7, which will get you$0.5. 20 times 25 is 500, so you will also time the $0.5 by 25 which will get you $12.5
Your parents gave you $50 to take your brother and sister to the movies. Your ticket cost $8.25 and your siblings cost $4.25. If you spent an additional $20 on soda and popcorn, how much money did you bring home with you?
$50
$13.25
$39.75
$10.25
Answers
Estimate the r- value for each scatterplot
Answers
a recipe calls for 24 fluid ounces of light whipping cream. if anthony has 1.5 pints of whipping cream in his refrigerator does he have enough for the recipe
Answers
Answer:
Yes
Step-by-step explanation:
He has 24 fluid ounces. You know this because in 1 pint, there are 16 fluid ounces. In half of one pint there are 8 ounces. 16 + 8 = 24 oz
I hope this could help!
Answer:
yes and he will have 4.8228 fluid ounces left over
Step-by-step explanation:
1.5 pints + 28.8228 US fluid ounces
What is the equation of the line that passes through the point (-3,-6) and (2,-2)
Answers
Answer:
[tex]y=\frac{4}{5}x-\frac{18}{5}[/tex]
Step-by-step explanation:
Hi there!
We want to find the equation of the line that passes through the point (-3, -6) and (2, -2)
There are 3 ways to write the equation of the line:
In slope-intercept form, which is y=mx+b, where m is the slope and b is the y interceptIn point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is a pointIn standard form, which is ax+by=c, where a, b, and c are integer coefficients, but a and b cannot be zero, and a cannot be negativeThe easiest way would either be slope-intercept or point-slope form, but let's write the equation in slope-intercept form, since it's the most common way
So we'll need to find the slope
The formula for the slope calculated from 2 points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
We have everything needed to find the slope, let's just label the values of the points to avoid any confusion:
[tex]x_1=-3\\y_1=-6\\x_2=2\\y_2=-2[/tex]
Now substitute these values into the formula. Remember that m is the value of the slope:
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{-2--6}{2--3}[/tex]
Simplify the fraction:
m=[tex]\frac{-2+6}{2+3}[/tex]
Add the numbers together:
m=[tex]\frac{4}{5}[/tex]
So the slope of the line is 4/5
Let's plug it into the formula y=mx+b, since we now know the value of m
y=[tex]\frac{4}{5}[/tex]x+b
Now let's find b
As the equation passes through both (-3, -6) and (2, -2), we can use either point to help solve for b
Either point works, but let's take (2, -2) for instance
Substitute 2 as x and -2 as y
-2=4/5(2)+b
Multiply
-2=8/5+b
subtract 8/5 from both sides
-18/5=b
Now substitute -18/5 as b into the equation:
[tex]y=\frac{4}{5}x-\frac{18}{5}[/tex]
Hope this helps!
plsss help me with this:((((
Answers
Answer: c. x + 3
Step-by-step explanation:
The first equation tells us the total area of the cloth. The second is the area of each piece. Divide the total area by the piece area to determine how many individual pieces can be made.
(x^3 + 27) can be factored into:
(x+3)(x^2 - 3x + 9) [Not easy, but true]
[(x+3)(x^2 - 3x + 9)]/(x^2 - 3x + 9)
(x^2 - 3x + 9) is on both sides, so it cancels, leaving (x + 3)
pls help me with this question
Answers
n = - 8/3
Decimal Form:
n = - 2.6
Mixed Number Form:
n = - 2 2/3
Find the values of m for which the equation
x^2 +2mx + 9 = 0 has no real roots
Answers
Answer:
Interval notation for m: (-3,3)
Inequality notation: -3<m<3
In words: Anything between -3 and 3 without including either -3 or 3.
Step-by-step explanation:
If we want no real roots then b^2-4ac must be less than 0.
a=1
b=2m
c=9
These values were found by comparing your equation to ax^2+bx+c=0.
b^2-4ac<0 is what we are trying to satisfy
(2m)^2-4(1)(9)<0
4m^2-36<0
Divide both sides by 4:
m^2-9<0
Add 9 on both sides:
m^2<9
m^2<9 when m<3 and m>-3.
Interval notation (-3,3).
jerry has 3,572 live chickens in his poultry farm.if there are 38 boxes , how many chickens must go in each box?
Answers
Answer: 94 live chickens go in each box.
Step-by-step explanation: 3,572 divided by 38 = 94 so 94 live chickens go in each box.
hope this helps :)
Can someone pls help me with this
Answers
Answer:
were is the qn?
Step-by-step explanation:
How do you show that x=6 is an true equation ?
Answers
x = 6 can be represented on the number line and hence it is real
Step-by-step explanation:
by simply plugging in 6 for x thus
x=6 becomes 6=6 which is true
4/9 plus -6/9
PLS I NEED HELP ASAP
Answers
Answer:
-2/9
Step-by-step explanation:
Since the denominators are the same, we can combine like terms
4/9 + (-6/9)
-2/9
[tex] \: \: \: \: \: \: [/tex]
[tex] = - \frac{2}{9} [/tex]
Step-by-step explanation:
[tex] \frac{4}{9} + \frac{ - 6}{9} [/tex]
write all numerators above the common denominator[tex] \frac{4 - 6}{9} [/tex]
calculate the difference[tex] \frac{ - 2}{9} [/tex]
[tex]use \: \: \frac{ - a}{b } = \frac{a}{b} = - \frac{a}{b} \: \: \: \: to \: \: rewrite \: \: the \: \: fraction[/tex]
[tex] = - \frac{2}{9} \\ \\ or \: \: in \: \: alternate \: form \\ \\ - 0.2[/tex]
hope it helps[tex] \: \: \: \: \: \: [/tex]
A garden swimming pool with a cuboidal shape is 8m long, 4m wide and 150 cm deep. The pool which is partially filled has 40m cube of water in it
Answers
At the craft store, Ivan bought a bag of orange and purple marbles. The bag contained 48 marbles, and 75% of them were orange. How many orange marbles did Ivan receive?
Answers
Answer:
jjjjjjjjjjjjjjjjjjjjjjjj
Leonardo da Vinci's portrait the Mona Lisa is
2 feet 6 inches long and 1 ft 9 inches wide.
Janelle has a refrigerator magnet of the
painting that is 3.5 cm wide. What is the
length of the magnet?
Answers
Answer:
the length of the magnet is 5cm
Step-by-step explanation:
first convert the feet into inches: 2ft 6in=30in, 1ft 9in=21in
then convert inches into centimeters (times by 2.5): 30*2.5=75cm 21*2.5=52.5
then divide 52.5 by 3.5 to get a proportion: 52.5/3.5=15
then divide 75 by 15: 75/15=5cm
Determine the value of x.
Answers
Answer:
x = 16
Step-by-step explanation:
46° and (3x - 2)° are alternate angles and are congruent , so
3x - 2 = 46 ( add 2 to both sides )
3x = 48 ( divide both sides by 3 )
x = 16
could you show me the step please and thank you
Answers
[tex]\dfrac{(2 x^{-3} y^{-2})^5}{(6x^{-1} y^{-8})^2}\\\\\\=\dfrac{32x^{-15} y^{-10}}{36 x^{-2} y^{-16}}\\\\\\=\dfrac{8}{9} \left(\dfrac{x^{-15}}{x^{-2}} \right) \left(\dfrac{y^{-10}}{y^{-16}} \right)\\\\\\=\dfrac 89 \left(x^{-15+2} \right) \left(y^{-10 +16} \right)\\\\\\=\dfrac 89 \cdot x^{-13} \cdot y^6\\\\\\=\dfrac{8y^6}{9x^{13}}[/tex]
7. The perimeter of a rectangular pool is 70 meters. If the width of the pool
is 12 meters, then find its length.
Answers
Answer:
23 meters
Step-by-step explanation:
You would subtract 24 from 70, and then divide by two.
70-24=46
46/2 = 23
> 70 = 2length + 24
Subtract 24 from both sides
> 46 = 2length
Divide by 2
> 23= length
The length of the pool is 23 meters
What is the prime factorization of 585?
585=
×
×
×
help pls im not thatgood at math
Answers
Answer:
3^2 * 5 * 13
Step-by-step explanation:
585
= 5 * 117
= 5 * 3 * 39
= 5 * 3 * 3 * 13
= 3^2 * 5 * 13
Answer:
3×3×5×13 that's the answer
Step functions
I don’t get what’s it’s trying to tell me to do not do I know where to begin
Answers
Answer:
[7.8] = 8
[0.75] = 1
...
Step-by-step explanation:
step function takes the value of the greatest integer
HELP ASAP!!! What is the measurement of where it says 41? I’m not sure if it’s in Feet or meters
Answers
Answer:
inches
Step-by-step explanation:
pretty sure that says 41 inches because at 36 it says 3 feet and 12 inches = 1 feet, so 36 inches equal 3 feet. The measurement would be inches.
Please help ASAP!! I am in desperate need and please don’t just do this for points
Answers
Answer:
[tex]106 yd^2[/tex]
Step-by-step explanation:
Answer is attached. Let me know if you would like another explanation that would yield the same solution.
Side AB of a parallelogram ABCD is produced upto point E. If m<CBE = 35°, find m<ADC.
Answers
Answer:
The measure of ∠ADC = 145°
Step-by-step explanation:
ABCD is a Parallelogram.
AB is produced to E .
∠CBE = 35°
We know that
∠ABC + <CBE = 180[tex]\degree[/tex]
Since , they are linear pair
➜ ∠ABC + 35° = 180°
➜ ∠ABC = 180°-35°
➜ ∠ABC = 145°
We know that
In a Parallelogram, Opposite angles are equal.
➜ The opposite angle of ∠ABC = ∠ADC
➜ ∠ADC = 145°
Therefore, The measure of ∠ADC = 145°
Read more:Similar Questions
In the accompanying diagram of the parallelogram ABCD, AB is extended to E such that CB is congruent to CE. If m< ADC = 100, what is m<CEB?
https://brainly.com/question/22056209?referrer