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mr Goodwill [35]
3 years ago
14

Which function in vertex form is equivalent to f(x) = 4 + x2 – 2x?

Mathematics
2 answers:
alisha [4.7K]3 years ago
6 0

Answer:

option A

f(x) = (x – 1)2 + 3

Step-by-step explanation:

Given in the question a function,

f(x) = 4 + x² – 2x

<h3>Step 1</h3>

f(x) = 4 + x² – 2x

here a = 1

        b = -2

        c = 4

<h3>Step 2</h3>

x = -b/2a

h = -(-2)/2(1)

h = 2/2

h = 1

Step 3

Find k

k = 4 + 1² – 2(1)

k = 3

Step 4

To convert a quadratic from y = ax² + bx + c form to vertex form,

y = a(x - h)²+ k

y = 1(x - 1)² + 3

y = (x - 1)² + 3

<h3></h3>

Mashutka [201]3 years ago
3 0

ANSWER

The vertex form is

f(x)  =  {(x - 1)}^{2}  + 3

EXPLANATION

The given function is

f(x)  = 4 +  {x}^{2}  - 2x

This is the same as:

f(x)  =  {x}^{2}  - 2x + 4

We add and subtract the square of half the coefficient of x.

f(x)  =  {x}^{2}  - 2x +  {( -1 )}^{2}  - {( -1 )}^{2}   + 4

f(x)  =  {x}^{2}  - 2x +  1    - 1  + 4

The first three term is a perfect square trinomial:

f(x)  =  {(x - 1)}^{2}    + 3

The vertex form is

f(x)  =  {(x - 1)}^{2}    + 3

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Step-by-step explanation:

16.

points are (0,-3),(2,1),(4,-3)

eq. of line through (0,-3) and (2,1) is

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or y+3=2x

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as the line is dotted so either < or >.

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put x=0,y=0

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which is true as graph lies above the line.

again eq. of line through (2,3) and (4,4) is

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so inequality is true as shaded portion is above and left of the line.

so two inequalities are

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and x-2y≤-4

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