SOLUTION: A function is defined by g:x=ax²+bx+2 where a and b are constants. If g(-2)=6 and g(3)=11, Find the values of a and b

Algebra.Com
Question 1196172: A function is defined by g:x=ax²+bx+2 where a and b are constants. If g(-2)=6 and g(3)=11, Find the values of a and b
Found 4 solutions by MathLover1, josgarithmetic, math_tutor2020, MathTherapy:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

A function is defined by:
where and are constants

If

............solve for

............simplify

...............eq.1


and if , we have






................eq.2

from eq.1 and eq.2 we have



-> will be true if

go to ................eq.2, plug in and we get

the values of and are and respectively

and your function is:





Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Maybe you mean , and for known points (-2,6) and (3,11) ?


Using the given points,


and steps to solve for a and b,




Add corresponding members:


and you can easily solve for b,.....
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Plug in x = -2
g(x) = a*x^2 + b*x + 2
g(-2) = a(-2)^2 + b(-2) + 2
g(-2) = a(4) + b(-2) + 2
g(-2) = 4a - 2b + 2
6 = 4a - 2b + 2
6-2 = 4a - 2b
4 = 4a - 2b

Let's solve for b
4 = 4a - 2b
4+2b = 4a
2b = 4a-4
b = 4a/2-4/2
b = 2a - 2

Now plug in x = 3
g(x) = ax^2 + bx + 2
g(3) = a(3)^2 + b(3) + 2
11 = 9a + 3b + 2

From here, plug in b = 2a - 2 and solve for 'a'
11 = 9a + 3b + 2
11 = 9a + 3(2a-2) + 2
11 = 9a + 6a-6 + 2
11 = 15a-4
15a-4 = 11
15a = 11+4
15a = 15
a = 15/15
a = 1

Then,
b = 2a-2
b = 2(1)-2
b = 2-2
b = 0


Answers:
a = 1
b = 0
The function is g(x) = x^2+2
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
A function is defined by g:x=ax²+bx+2 where a and b are constants. If g(-2)=6 and g(3)=11, Find the values of a and b
I hope for your sanity that you didn't pay any attention to that woman's method of solving this porblem. She has this habit
of solving a variable in terms of another variable in fractional form, which is TOTALLY UNNECESSARY and LUDICROUS!! 

g(-2) = 6 signifies that x = - 2 when y = 6. We then have: 
   
  ---- Substituting - 2 for x
g(- 2) = 4a - 2b + 2
     6 = 4a - 2b + 2 ----- Substituting 6 for y, or g(- 2)  
     4 = 4a - 2b____2(2) = 2(2a - b)_____2 = 2a - b ----- eq (i)

Likewise,  g(3) = 11 signifies that x = 3 when y = 11. We then have: 
 
  ----- Substituting 3 for x
 g(3) = 9a + 3b + 2
   11 = 9a + 3b + 2 ----- Substituting 11 for y, or g(3)  
    9 = 9a + 3b____3(3) = 3(3a + b)_____3 = 3a + b ----- eq (ii)

We then have:
2 = 2a - b ----- eq (i)
3 = 3a + b ----- eq (ii
5 = 5a ---- Adding eqs (i) & (ii)


3 = 3(1) + b ------ Substituting 1 for a in eq (ii)

RELATED QUESTIONS

The function of g is defined as g(x)=ax^2+b where a and b are constants. If g(2)=3 and... (answered by rothauserc)
Consider the polynomial F(x)=4x^3+(a+1)x^2+x-5b and G(x)=4x^3-ax^2+bx-2, where a and b... (answered by ikleyn)
Find a size change that maps f(x)=ax^2 onto g(x)=bx^2 where a and b are non-zero real... (answered by Alan3354)
The functions f and g are defined by these sets of input and output values. (answered by issacodegard)
x –1,1,2 f(x) 729,9,1 Q65 The table above shows some values for the function... (answered by greenestamps)
The graph of the function is given (a) Find g(-4), g(-2), g(0), g(2), and g(4). (b)... (answered by solver91311)
Consider the function F and G defined by F(x)={{{(x-6)/(2x+5)}}} and... (answered by solver91311)
Suppose that the functions g an h are defined as follows. g(x)=(-3+x)(-3+x) h(x)=2-8x (answered by josgarithmetic)
1. The function f(x) and g(x) are defined by f(x)=2^x and g(x)= log2(1-2x) a. Write down (answered by solver91311)