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Ugo [173]
4 years ago
6

Which of the following graphs is described by the function given below? y = 2x 2 + 6x + 3

Mathematics
1 answer:
Alla [95]4 years ago
8 0

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

y=2x^{2}+6x+3

This is the equation of a vertical parabola open up

The vertex is a minimum

Convert to vertex form

Complete squares

y-3=2x^{2}+6x

Factor the leading coefficient

y-3=2(x^{2}+3x)

y-3+4.5=2(x^{2}+3x+2.25)

y+1.5=2(x^{2}+3x+2.25)

Rewrite as perfect squares

y+1.5=2(x+1.5)^{2}

The vertex is the point (-1.5,-1.5)

Find the zeros of the function

For y=0

2(x+1.5)^{2}=1.5

(x+1.5)^{2}=3/4

square root both sides

x+\frac{3}{2} =(+/-)\frac{\sqrt{3}}{2}

x=-\frac{3}{2}(+/-)\frac{\sqrt{3}}{2}

x=-\frac{3}{2}(+)\frac{\sqrt{3}}{2}=\frac{-3+\sqrt{3}}{2}=-0.634

x=-\frac{3}{2}(-)\frac{\sqrt{3}}{2}=\frac{-3-\sqrt{3}}{2}=-2.366

Find the y-intercept

For x=0

y=3

The y-intercept is the point (0,3)

therefore

The graph in the attached figure

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Graph the line with slope-2/3<br> passing through the point (-5, -4),
Orlov [11]

Answer:

The figure is attached down

Step-by-step explanation:

To graph a line you must have its equation

The form of the linear equation is y = m x + b, where

  • m is its slope
  • b is the y-intercept (y at x = 0)

∵ The slope of the line is  -\frac{2}{3}

∴ y = -\frac{2}{3} x + b

- To find b substitute x and y in the equation by the coordinates

   of a point on the line

∵ The line passing through point (-5 , -4)

∴ x = -5 and y = -4

∵ -4 =  -\frac{2}{3} (-5) + b

∴ -4 = \frac{10}{3} + b

- Subtract  \frac{10}{3} from both sides

∴ -\frac{22}{3} = b

∴ y = -\frac{2}{3} x - \frac{22}{3}

To draw the line substitute x by any two values and find their ys

∵ x = -2

∴ y = -\frac{2}{3} (-2) - \frac{22}{3}  

∴ y = -6

∴ The line passing through point (-2 , -6)

∵ x = 1

∴ y = -\frac{2}{3} (1) - \frac{22}{3}  

∴ y = -8

∴ The line passing through point (1 , -8)

∵ x = 4

∴ y = -\frac{2}{3} (4) - \frac{22}{3}  

∴ y = -10

∴ The line passing through point (4 , -10)

Now we can make a table to draw the line

→  x  : -5  :  -2  :  1  :  4

→  y  : -4  :  -6  : -8 :  -10

Plot the points on the graph paper and draw the line

<em>Look to the attached graph</em>

4 0
4 years ago
What is the value of f(x) when x=3?
zvonat [6]

I'm not good at math but I think is 3f because you'll be multiplying f(unknown #) by 3 so f(x) would be 3f

5 0
3 years ago
I need help whats 5/8 + 14 the 5/8 is a fraction
Katarina [22]

Hey there!

5/8 + 14 = ?

We can say 14 is equal to 14/1 beause it doesn't have a denominator and we will need to solve for your equation

14 * 8 = 112 (upcoming numerator for now)

8 * 1 = 8 (upcoming denominator for now)

5 stays alone

New equation 5 + 112 / 8

5 + 112 = 117 (numerator)

8 = 8 (demominator)

Answer: 117/8 (if you're looking for the improper fraction version) ; 14 5/8 (if you're looking for the mixed number version) ; 14.625 (if you're looking for the decimal version of it)

⬆ ANY one of these choices SHOULD work

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

6 0
4 years ago
Read 2 more answers
What's the pattern rule for 8 12 24 60 168?
lilavasa [31]
He changes are 3 times larger each time.

8 changed by 4 to get to 12.

12 changed by 12 to get to 24.

24 changed by 36 to get to 60.

60 changed by 108 to get to 168.
6 0
4 years ago
GIVING 40 POINTS!! PLEASE ANSWER FAST WILL REPORT IF WRONG!!!
Leni [432]

Answer:

Step-by-step explanation:

1. Proportion.

\frac{3}{7.5}  =  \frac{1}{x}

2.Lets cross multiply.

3x=7.5

3.Solve

3x=7.5\\divide 3x -on- both-sides\\\\

________________

x=2.5

1=2.5\\1:2.5

Hope this helps :)

6 0
3 years ago
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