Question

The table shows some of the values of a function of the form y=ax^2+bx+c which is the value of c, the constant, the constant for the function?

Answer 1

Answer:

$c=8$

Step-by-step explanation:

Given: $y=ax^2+bx+c$

To find: c

Solution:

At $x=4,y=48$:

$48=16a+4b+c$    (i)

At $x=5,y=73$:

$73=25a+5b+c$    (ii)

At $x=6,y=104$:

$104=36a+6b+c$   (iii)

On subtracting (i) and (ii),

$25=9a+b$   (iv)

On subtracting (i) and (iii),

$56=20a+2b\\\\28=10a+b \,\,\,\,(v)$

On subtracting (iv) and (v),

$a=3$

Put a=3 in (iv)

$25=9(3)+b\\25=27+b\\25-27=b\\-2=b$

Put $a=3,b=-2$ in (iii)

$104=36(3)+6(-2)+c\\104=108-12+c\\104=96+c\\104-96=c\\8=c$