Find the values for this formula...?

Question

The graph of y= (a/x) + bx^2 has an x-intercept of 1/2 and contains the point (1,7). Find the values of a and b.

Answer 1

What this means is that, since there is an x-intercept at x = ½, the corresponding y value at the x-intercept is 0.  So we can substitute the x and y values into the equation to find a and b:

y= (a/x) + bx²

0 = a/(½) + b (½)²

0 =  a/(½) + b (¼)

0 = 2a + b/4

0 = 8a + b. (We multiplied both sides by 4.)

-b = 8a

b = -8a

Now that we have b in terms of a, we can use the other point, (1, 7), to determine a, then ultimately the value of b also:

y= (a/x) + bx²

7 = a/(1) + (-8a)(1)²

7 = a - 8a

7 = -7a

-1 = a.

Now we can find the value of b:

b = -8a

b = -8 (-1)

b = 8.

To see if these calculated values work, plug them into the original equation, and see if the correct values for y result

y= (a/x) + bx²

0 = -1/(½) + (8)(½)²

0 = -2 + 8/4

0 = -2 + 2

0 = 0

Our values for a and b yield a balanced equation for the point (½, 0).  Now let's check the second point, (1, 7):

y= (a/x) + bx²

7 = (-1)/(1) + (8)(1)

7 = -1 + 8

7 = 7

The equation also balances for the point (1, 7), so we seem to have the correct values for a and b: a = -1, and b = 8.

  

Answer 2

Hello there!

If all the data that you are providing me with is correct, then my solution should be write!

y=(a/x) + bx^2

points:

(1/2;0) ___ x-intercept of 1/2

(1,7)

Unknown= a; b

Step 1:

we substitute the point (1/2;0) into the equation

y=(a/x) + bx^2

0=(a/0.5) + b(1/2)^2

0=2a + b(1/4)

0=2a + (b/4)

we divide each side by 2

0=a + (b/2)

Step 2:

we substitute point (1,7) into the equation

y=(a/x) + bx^2

7=a + b

0=a + b - 7

Step 3:

now we have 2 equations which equal to 0

0=a + (b/2)

0=a + b - 7

this means that the right sides of the 2 equations above are equal to each other as well

a + (b/2)=a + b - 7

move "a" from the right side to the left side and move "b/2" from the left side to the right side

a-a= - (b/2) + b - 7

0=  - (b/2) + b - 7

now we must move 7 from right side to the left

7= b - (b/2)

7= b/2

b=14

now we have the value of one variable...

and using that value we are going to find the value of the other variable

we substitute b=14 into the equation 7=a+b

7=a+b

a=b-7

a=14-7

a=7

Therefore:  the values of a and b are the following: a=7 and b=14

Hope this helps! If you have any questions do not hesitate to ask!

Answer 3

the standard equation is y = mx + b

and you just have to plug in for the values so you have two ordered pairs (x,y) and the x-intercept of 1/2 (1/2,0) your equation has an x and y plug them in

7= a/1 + b(1)^2 simplified as 7 = a + b (a/1=a)

and 0= a/(1/2) + b/4 simplified as 0= 2a + b/4

now set the two equations equal to one value a or b

in the first b= 7 - a and in the second b= -8a after simplification now you can set both of those equations equal to each other

b=b and 7 - a= -8a, -a = 1 or a = -1

and then take one of those equations you had and substitute b and you will get b= 7 - (-1) or b=8

then for you to be sure the answers are right then you will have to substitute a and b in the original equation

7= -1/1 + 8(-1)^2 which is 7= -1 + 8 thus 7=7

Answer 4

my brain hurts !

Answer 5

say please.  

Answer 6

The x-intercept is when y = 0, x = 1/2

Substitute those values of x and y into the equation.

Substitute 1 and 7 for x and y to give you another version of the equation.

Solve the system of equations.