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Arlecino [84]
4 years ago
12

Write y=2x^2+12x+14 In vertex form

Mathematics
1 answer:
ratelena [41]4 years ago
7 0

Answer:

\large\boxed{y=2(x+3)^2-6}

Step-by-step explanation:

The vertex form of a parabola f(x) = ax² + bx + c:

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

(h, k) - vertex

h=\dfrac{-b}{2a}\\\\k=f(h)

We have the equation:

y=2x^2+12x+14\\\\a=2,\ b=12,\ c=14\\\\h=\dfrac{-12}{2(2)}=\dfrac{-12}{4}=-3\\\\k=f(-3)=2(-3)^2+12(-3)+12=2(9)-36+12=18-36+12=-6

Finally:

y=2(x-(-3))^2+(-6)=2(x+3)^2-6

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Step-by-step explanation:

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2 years ago
Given the table of data, determine the function that would most appropriately model the data. x 0 1 2 3 f(x) 1.5 2 2.5 3 linear
azamat

Answer:

  linear

Step-by-step explanation:

The x-values are evenly spaced (1 apart), so it is helpful to look at the differences of the f(x) values.

Successive f(x) values all differ by the constant 0.5, a characteristic of a linear function.

_____

<em>Comment on differences</em>

The differences of successive y-values are called "first differences". The differences of those are called "second differences". And the differences of those are "third differences." The "degree" of the differences that are constant is the degree of the function describing the sequence.

That is, a sequence (like this one) with constant first differences can be described by a first-degree polynomial, a linear function. If third differences are constant, the sequence is described by a third-degree polynomial, a cubic function.

A square root function will have first differences that decrease by a decreasing amount. Successive differences of differences will continue to decrease, never becoming constant.

An exponential function will have first differences with a common ratio.

3 0
3 years ago
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lana66690 [7]

Answer:

∠A = 88°

Step-by-step explanation:

= 180° - (50° + 38°)

= 180° - 88°

= 92°

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2x/x-3 - 6/x-3 . I need a step by step explanation , please
Harman [31]
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2(x-3)/(x-3)  the (x-3)s cancel out leaving

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What this all means is that that expression will equal 2 for all real values of x other than 3.
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d1i1m1o1n [39]

Answer:

{x}^{2}  + 6x + 9 \\

Step-by-step explanation:

{(x + 3)}^{2}  \\ (x + 3)(x + 3) \\ x(x + 3) + 3(x + 3) \\  {x}^{2}  + 3x + 3x + 9 \\  {x}^{2}  + 6x + 9 \\

5 0
3 years ago
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