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kompoz [17]
3 years ago
7

What’s 8x squared + 4 in vertex form

Mathematics
1 answer:
Nataly [62]3 years ago
7 0

expression  8x squared + 4  or , 8x^2+4 in the vertex form is  8(x+0)^2+4 .

<u>Step-by-step explanation:</u>

Here we have , to convert expression  8x squared + 4  or , 8x^2+4 in the vertex form . Let's find out:

Let  y=8x^2+4 ,

⇒   y=8x^2+0(x)+4

Comparing this equation with y = ax^2+bx+c we get ;

a=8\\b=0\\c=4

Now , We know that  the vertex form of a parabola is ;

⇒ a(x+d)^2+e     ............(1)

Substitute the values of  a  and  b  into the formula d =\frac{b}{2a}

⇒ d=\frac{0}{2(8)} =0

Now , Value of e is ;

⇒ e= c- \frac{b^2}{4a}

⇒ e=4

Putting value of a, d ,e in equation (1) we get ;

⇒ a(x+d)^2+e  

⇒ 8(x+0)^2+4

Therefore ,  expression  8x squared + 4  or , 8x^2+4 in the vertex form is  8(x+0)^2+4 .

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So first off, the most important thing in Geometry is to know the relationship between angles and lines. A vertical line is 180 degrees, a line bisecting something means that whatever is bisected is equal to the other side, vertical angles are equal to each other, etc. Once you understand these it will be a breeze. Make sure you always write down the numbers you find out on the problem in its place so you can keep on track and visualize it better!

8) The 2 angles represented by the equations are being bisected by a vertical line. So that means they are equal to each other and we can solve by putting that into an equation. 5x-46=2x+5, 3x-46=5, 3x=51, x=17. Now just plug in 17 for x. 5(17)-46, 85-46=39. <PQR=39

9) A linear pair is just 2 angles that make a 180 degree angle so, 1, 4, & 5

10) A vertical angle is an angle that is equal and opposite to the other. In this case the only clear one is 1 & 4 (Answer) but angles 2 and 3, when added, would equal angle 5.

11) Supplementary means it equals 180 degrees so the same as #9. 1 & 5, 4 & 5

12) Set 3x+20 and y-20 have different variables, it is easier to use x and 3x+20.Both of these angles form a linear pair, which means they equal 180 so set both of them equal to it. 3x+20+x=180. Combine like terms. 4x+20=180, 4x=160, x=40. Now plug in 40 for x. Since one angle is just x and x=40, subtract that from 180 to find the other angle. We now know y-20=140 so we can simply work out the equation. y-20=140, y=160. Our final answer is x=40 and y=160.

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I hope I didn't get anything wrong I was in a bit of a rush. Just remember the rules and the relationships and you'll do great!


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