Algebra, Equations etc HELP PLEASE?

Question

The quadratic equation y = ax² + bx + c = 0 is used in signal processing to represent a more complex signal. This function passes through the points (in the form (x,y))(0,0), (2,5) and (6,10). Write down simultaneous equations in a, b and c and solve them to find the function.

Help please how would i work it out??!!!

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Answer 1

When plotting graphs, the first number inside the brackets is the value of x and the other number is the value of y. The The first point given is x=0 , y=0. Now replace the letters x and y in the given equation with their given values.

0 = 0 + 0 + c Therefore c = 0 (Note: Any number multiplied by 0 is equal to 0.

Repeat the procedure with the other given points.

Second point x=2 and y = 5

hence 5 = 2^2a + 2b + c and since the value of c is 0

5 = 4a +2b Therefore 4a + 2b = 5 ...............(1)

The third point is x=6 and y = 10

Hence 10 = 36a + 6b + 0

Therefore 36a + 6b =10 ..............(2)

Multiply equation (1) by 3 to give

12a + 6b = 15 .....................(3)

Now subtract equation (3) from equation (2)

24a = -5 (Note: 6b - 6b = 0 and 10 - 15 = -5 )

a = - (5/24) = - 0.208333

Substituting this value in equation (1)

-0.208333x4 + 2b = 5

2b = 5 + 0.833333 = 5.833333

Therefore b = 5.833333/2 = 2.91667

Same results obtained by using the 'Consys GraphPlots' program which in addition to plotting graphs you can calculate any given number of linear equations simultaneously.

Answer 2

At point (0,0): 0 = 0 + 0 +c -> c=0
At point (2,5): 5 = 4a +2b + c (but c=0) -> 4a + 2b = 5 (1)
At point (6,10): 10 = 36a + 6b + c -> 36a+ 6b = 10 (2)

(1)*9 36a +18b = 45 (3)
(2) 36a + 6b = 10
(3)-(2) 12b = 35 -> b = 35/12

Substitute in (1)
4a + 35/6 = 5 -> 4a = 5 - 35/6 = (30-35)/6 = -5/6 -> a = -5/24

so a = -5/24, b = 35/12, c=0

Answer 3

Okay, first of all, it's either y= ax² + bx + c and ax² + bx + c = 0. It's one, not both. They serve different purposes. One is used to graph, and the other is used to find the values.

Okay, first, take one of the points -- for example, (2, 5). In this case, x=2 and y=5.
Now, substitute those values in the equation y= ax² + bx + c. You will see that it now reads: 5= (2a)² + 2b + c, which then becomes: 5 = 4a² + 2b + c. Now, subtract both 5 and c from each side: -c = 4a² + 2b -5. Now multiply both sides by -1, and you have the value: c= -4a² - 2b + 5.

Do the same thing with the other two sets of points. For each, you should get a similar-looking equation for both the values of a and b. Finally, choose one variable to solve the numeric answer for, and plug the values of the other two variables into a single equation. (i.e. If you want to solve for a, use the equation that begins with "a=" and plug in the equation-values of b and c, and solve for the numeric value of a.

Afterwards, repeat the process for the next variable -- b, for example, but this time, plug in the equation-value of c and the numeric value of a. Finally, solve for c.

I know it sounds really complicated, but believe me, it's much easier to do than to explain.

Answer 4

For (0,0) : 0=a*0^2+b*0+c => c=0 => y=ax^2+bx
For (2,5) : 5=a*2^2+b*2 => 4a+2b=5 .....(*)
For (6,10) : 10=a*6^2+b*6 => 36a+6b=10 ......(**)
Solve the system from (*) and (**) and a=-5/24 b=35/12

Answer 5

Try (0,0):-
0 = 0 + 0 + c
c = 0
y = ax² + bx
5 = 4a + 2b

- 45 = - 36a - 18b
10 = 36a + 6b-----ADD
- 35 = - 12b
b = 35/12
5 = 4a + 70 / 12
4a = - 10 / 12
a = - 10 / 48 = - 5 / 24
y = (- 5 / 24).x² + (35 / 12).x

Answer 6

temporarily:take them as factors, locate the slope and discern all of it. intimately: a million. our objective is to locate the slope, slope (m) = (fifty 9.5-33.9)/(fifty 3-0) = 0.483 now y = mx + c y= 0.483x + c from the element (0.33.9) we get c = 33.9 y= 0.483x + 33.9 2. the fee of substitute is the by-product, yet it relatively is x and y. supposing x is the 365 days and y is the inhabitants then fee stands out as the by-product or slope it relatively is 0.483 3. might desire to comprehend what's x and y.(if x is 365 days and y is %) then see fifty 5 years might desire to be extra to 1950 to make it 2005 so x = fifty 5 now locate y, y= fifty 5*0.483+33.9=60.465%

Answer 7

lol I suck at math, good luck, or just go to a website that does it for you xx

Answer 8

i think you should try microsoft math.i tried it its really best.http://www.microsoft.com/math/