Question

The function g(n) = n2 − 20n + 95 represents a parabola.

Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points)

Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points)

Part C: Determine the axis of symmetry for g(n).

Answer 1

@Shadow

Answer 2

Did part A with dude yesterday but now need part B and C

Answer 3

I have to study for a quiz so I won’t be able to help you. Try tagging dude. I know there are easy websites that can help you find the vertex and axis of symmetry. I used them years ago. Also, a minimum just means the vertex is on the bottom, with the lines going up. Maximum means the vertex is the highest point, with the parabola going down.

Answer 4

g(n)= n^2-20n+95
Step 1: n^2 - 20n + 100
Step 2: (b over 2) ^2 So (-20 over 2) ^2=-10^2=100
Step 3: (n^2-20n=100)=95-100
Step 4: (n-10) (n-10)- 5
Step 5: (n-10)^2 - 5
Answer G(n)=(n-10)^2-5

Answer 5

@dude

Answer 6

Do you know what the vertex is?

Answer 7

yes

Answer 8

What is it?

Answer 9

hold on im pulling it up

Answer 10

(10,-5)

Answer 11

Mhm, and have you determined whether this is a minimum or a maximum?

Answer 12

I think its maximum because it goes from negative to positive

Answer 13

What do you mean from negative to positive

Answer 14

hold on imma show u what i have

Answer 15

^^if u look it goes down to up so that would make it maximum because it goes up to the positives

Answer 16

Maximum is when the vertex is the highest point. Does that seem to be the case?

Answer 17

Nu so it would be minimum because the vertex has negatives and it is not at its highest points

Answer 18

Think of it this way:

Maximum: Parabola opens down
Minimum: Parabola opens up

Answer 19

Ohhhh so

Its minimum because the vertext is not at its highest points and becuase the parabola opens up

Answer 20

Yes

Answer 21

*because

Answer 22

And it since it's the lowest point.

Answer 23

how do we know?

i know because if the vertex is in the negatives it means its at its lowest points so that would make the parabola open

Answer 24

A vertex can be in the negative and still be a maximum.

Answer 25

That's why you focus on these two qualifications:

Opens up/Opens down
Highest point/lowest point

It's positioning of the vertex in terms of pos/neg doesn't matter.

Answer 26

so how would you explain how you know if a vertex
could still be in negatives but still maximum

Answer 27

Because it's the highest point in the graph and the parabola opens down.

Answer 28

I know because its the lowest point in the graph and the parabola opens up

Answer 29

@dude can yew helps yeet

Answer 30

@dude e.e

Answer 31

Part C im on den one last question

Answer 32

In order to find axis of symmetry you have to use the this equation:
\(\large -\frac{b}{2a}\)

Remember: This equation is written as \(g(n)=ax^2+bx+c\)

Answer 33

i know so it would be (n-10) over -5?

Answer 34

cause the equation we finished yesterday is G(n)=(n-10)^2-5

Answer 35

Ah we're using the original equation for this one \(n^2 − 20n + 95\) As its written in standard form \(ax^2+bx+c\)

Answer 36

im confused now so we dont use our revised equation we use the original

Answer 37

We use the original

Answer 38

Its easier to solve for the vertex at least in my opinion

Answer 39

i have the vertex i need the axis symmetry

Answer 40

^^look up i already told shadow the vertex for part B

Answer 41

OHHHHHHHHH

Answer 42

Scratch what I just said, just look at the h value
Hint: \(g(n)=a(x-h)+k\)

Answer 43

Umm ok.....

Answer 44

\(g(n)=(n-10)^2-5\)
What is the h value?

Answer 45

10?

Answer 46

Right so x=10 is the axis of symmetry
This may help https://www.desmos.com/calculator/s7k0gr4pee

Answer 47

what? u just what IM SOOO CONFUSED how did it go from 10 being h to 10 being x

Answer 48

The rule for axis of symmetry: \(x=h\)
\(g(n)=(x-h)+k\)

The value of x for the line of symmetry is equal to the value of h on the vertex form for an equation

Answer 49

so
Part C: The Axis equals 10.

Answer 50

The axis of symmetry is when x=10, yes

Answer 51

Ok are you ready to finish da last question

Answer 52

give me a few mins, ill be right there. Post it though

Answer 53

ok