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algol [13]
3 years ago
10

The axis of symmetry for the function f(x) = –2x2 + 4x + 1 is the line x = 1. Where is the vertex of the function located?

Mathematics
2 answers:
Svetlanka [38]3 years ago
7 0

Answer:

(1,3)

Step-by-step explanation:

egoroff_w [7]3 years ago
5 0

Answer:

(1, 3)

Step-by-step explanation:

You are given the h coordinate of the vertex as 1, but in order to find the k coordinate, you have to complete the square on the parabola.  The first few steps are as follows.  Set the parabola equal to 0 so you can solve for the vertex.  Separate the x terms from the constant by moving the constant to the other side of the equals sign.  The coefficient HAS to be a +1 (ours is a -2 so we have to factor it out).  Let's start there.  The first 2 steps result in this polynomial:

-2x^2+4x=-1.  Now we factor out the -2:

-2(x^2-2x)=-1.  Now we complete the square.  This process is to take half the linear term, square it, and add it to both sides.  Our linear term is 2x.  Half of 2 is 1, and 1 squared is 1.  We add 1 into the set of parenthesis.  But we actually added into the parenthesis is +1(-2).  The -2 out front is a multiplier and we cannot ignore it.  Adding in to both sides looks like this:

-2(x^2-2x+1)=-1-2.  Simplifying gives us this:

-2(x^2-2x+1)=-3

On the left we have created a perfect square binomial which reflects the h coordinate of the vertex.  Stating this binomial and moving the -3 over by addition and setting the polynomial equal to y:

-2(x-1)^2+3=y

From this form,

y=-a(x-h)^2+k

you can determine the coordinates of the vertex to be (1, 3)

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Is negative 1/3 less than 1/5
nika2105 [10]
Negatives are always smaller then positives because negatives are less then 0. So, yes, -1/3 is less then 1/5
3 0
2 years ago
G(t)=(t+1) ^2-20.25 what are the zeros of the function
Vinil7 [7]

Step-by-step explanation:

g(t) = (t + 1)² − 20.25

0 = (t + 1)² − 20.25

20.25 = (t + 1)²

±4.5 = t + 1

t = -1 ± 4.5

t = -5.5 or 3.5

The zeros are (-5.5, 0) and (3.5, 0).

5 0
3 years ago
Alicia, Quentin, and Rosalyn are siblings. Alicia is the oldest sibling. Quentin is four years younger than Alicia. Rosalyn is t
tatiyna

Answer:

Alicia is 18years

Quentin is 14years

Rosalyn is 16years

Step-by-step explanation:

Let the age of Alicia be x

Let the age of Quentin be y

Let the age of Rosalyn be z

If the sum of the siblings’ ages, in years, is 48 then;

x+y+z = 48.... 1

If Rosalyn is two years older than Quentin then;

z =y+2 ..... 2

Also if Quentin is four years younger than Alicia then;

y = x-4 ... 3

From 3:

x = y+4 ... 4

Substitute 2 and 4 into 1 to have:

y+4+y+y+2 = 48

3y + 6= 48

3y = 48-6

3y= 42

y = 14

Since x= y+4

x = 14+4

x = 18

Since z = y+2

z = 14+2

z = 16year

This means that;

Alicia is 18years

Quentin is 14years

Rosalyn is 16years

6 0
2 years ago
Help ASAP!!!<br><br> Identify the correct trigonometry formula to use to solve for x.
Alex787 [66]

Answer:

cos(55) = 11/x

Step-by-step explanation:

We have the hypotenuse (x) and an angle adjacent to 55 (11). The only trigonometric formula that uses adjacent and hypotenuse is cosine (adjacent/hypotenuse), so that will be your answer.

4 0
3 years ago
Read 2 more answers
Whats 12*5+55= <br><br> ill mark asa brainliest
Aleksandr-060686 [28]
First do PEMDAS
There's no parenthesis. So move on to exponent. There's also no exponents. Move on to  multiplication. There it is. 

12×5=60.

There's no division so now next one is addition. Hey look! There is addition. 

60+55=115.

So 115 is your answer.
5 0
3 years ago
Read 2 more answers
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