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Nutka1998 [239]
3 years ago
11

The equation of a parabola is y=x^2-10x+27. Write the equation in vertex form

Mathematics
1 answer:
azamat3 years ago
4 0

Answer:

\large \boxed{y = (x - 5)^{2} + 2 }

Step-by-step explanation:

y = x² - 10x + 27

y = ax² + bx + c

This is the general form of the equation for a parabola.

We must convert it to the vertex form

y = (x - h)² + k, where (h,k) are the coordinates of the vertex.

We can do this by completing the square.

\begin{array}{rcll}y & = & x^{2} - 10x + 27 & \\y - 27 & = & x^{2} - 10x & \text{Subtracted 27 from each side}\\y - 27&= & x^{2} - 10x + 25 - 25 & \text{Added and subtracted (b/2)}^{2}\\y - 27&= & (x - 5)^{2} - 25 & \text{Wrote the first three terms as the square of a binomial}\\y& = & \mathbf{(x - 5)^{2} + 2} & \text{Added 27 to each side}\\\end{array}\\\text{The vertex form of the parabola is $\large \boxed{\mathbf{y = (x - 5)^{2} + 2 }}$}The figure below shows that your parabola has its vertex at (5,2).

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Cannon balls for an antique cannon are stacked next to it in four layers to form a square pyramid. How many cannon balls are in
labwork [276]
The amount of balls in a given layer can be found by squaring the layer it is in

4 layers
top layer (1st) is 1
2nd is 4
3rd layer is 9
4th is 16

add them up
1+4+9+16=30

30 in that pyramid
7 0
3 years ago
If Chloe is 22 her sister Bethany is 23 but there mum is 21 how are they her children
gayaneshka [121]

Answer:

3

Step-by-step explanation:

I think it three sometimes it's a trick question  

so its not number one or 2 because how are they her children so the answer is 3

3 0
2 years ago
Need help please thx you
erma4kov [3.2K]
$72.

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6 0
3 years ago
At the start of 2014, tim house was worth £100,000 the value of the house increases by 10%per every year work out the value of h
kotykmax [81]

Answer:

$146410

Step-by-step explanation:

The formula for calculating future value:

FV = P (1 + r)^n

FV = Future value  

P = Present value  

R = interest rate  

N = number of years

100,000 x (1.1)^4 = $146410

4 0
2 years ago
A triangle is shown.
aleksklad [387]

Using the Pythagorean Theorem, it is found that the unknown side length of the triangle is of 7.9 cm.

<h3>What is the Pythagorean Theorem?</h3>

The Pythagorean Theorem relates the length of the legs l_1 and l_2 of a right triangle with the length of the hypotenuse h, according to the following equation:

h^2 = l_1^2 + l_2^2

Researching this problem on the internet, we have that:

  • The unknown side length is of a leg of x.
  • The other leg is of 9 cm.
  • The hypotenuse is of 12 cm.

Hence:

x² + 9² = 12²

x = sqrt(12² - 9²)

x = 7.9 cm.

The unknown side length of the triangle is of 7.9 cm.

More can be learned about the Pythagorean Theorem at brainly.com/question/654982

#SPJ1

4 0
2 years ago
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