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marusya05 [52]
3 years ago
9

What is f(x) = 8x2 + 4x written in vertex form?

Mathematics
1 answer:
Pepsi [2]3 years ago
8 0
First of all, you need to complete the square of \(x\)

and this could be done as follows:

f(x)=8[x^2+0.5x]
     =8[x^2 + 0.5x + (0.5/2)^2 - (0.5/2)^2]
     =8[(x^2 + 0.5x +1/16) - 1/16]
     =8[(x+0.25)^2 - 1/16]


And our parabola has the vertex form of this:
 
     f(x)=8(x+ \frac{1}{4})^2 -  \frac{1}{2}

and according to the chart I attached, the vertex is (-0.25,-0.5)


Tell me <span>if there is any difficulty faces you!</span>

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How do I solve for x?
notka56 [123]
Solving:
\frac{3+4x}{2} + \frac{5-x}{3} = \frac{29}{6}
Make the Least Common Multiple (2,3,6)
2,3,6\:|2
1,3,3\:|3
1,1,1\:|\underline{2*3=6}


<span>Replace denominators and resolve:
</span>\frac{3+4x}{2} + \frac{5-x}{3} = \frac{29}{6}
\frac{3(3+4x)}{6} + \frac{2(5-x)}{6} = \frac{29}{6}
Cancel the dominators
\frac{3(3+4x)}{\diagup\!\!\!\!6} + \frac{2(5-x)}{\diagup\!\!\!\!6} = \frac{29}{\diagup\!\!\!\!6}
3(3+4x) + 2(5-x) = 29
9 + 12x + 10 - 2x = 29
12x - 2x = 29 - 9 - 10
10x = 20 - 10
10x = 10
x =  \frac{10}{10}
\boxed{\boxed{x = 1}}\end{array}}\qquad\quad\checkmark


7 0
3 years ago
What is six times more than three times a number is that number increased by 24. Find the number. Write an equation. And find x
Lubov Fominskaja [6]

Given the information, you can only write an expression and simplify it:

6(3(x+24))

6(3x+72)

SOlution: 18x+432

I hope I helped you with your solution! If you could give me brainliest, I would be very thankful!

4 0
3 years ago
The sum of three consecutive even integers is -114.
Alika [10]
The sum of three consecutives is b 
5 0
3 years ago
Miguel and Jian go to a restaurant and eat dinner. The total cost of the meal is $75. Miguel and lar decide to split
natima [27]

Answer:

x+ y = 75

Step-by-step explanation:

The both paid a total of 75.

Therefore, in order to get 75 you would need to add the amount each of them paid.

8 0
3 years ago
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How can you show the two objects are proportional.
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Their shape and size
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3 years ago
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