Question

Which equation does the graph of systems of equations solve?

Answer 1

b

Explanation:

Answer 2

The equation which solves the graph of system of equation is:

`x^2+6x+8=-x^2-8x-16`

Explanation:

• The blue parabola passes through:

(-4,0),(-3,-1) and (-2,0)

Let the equation of parabola be:

`y=ax^2+bx+c`

Now, when we take the point (-4,0) we have:

`16a-4b+c=0----------(1)`

when we take the point (-3,-1) we have:

`9a-3b+c=-1---------(2)`

and when we take the point (-2,0) we have:

`4a-2b+c=0-----------(3)`

on subtracting equation (3) from equation (1) we have:

`12a-2b=0\\\\i.e.\\\\12a=2b\\\\i.e.\\\\b=(12a)/(2)\\\\i.e.\\\\b=6a`

and on putting the value of b in equation (3) we have:

`4a-2(6a)+c=0\\\\i.e.\\\\4a-12a+c=0\\\\i.e.\\\\c=8a`

Now, on putting the value of b and c in terms of a in equation (2) we have:

`9a-3(6a)+8a=-1\\\\i.e.\\\\9a-18a+8a=-1\\\\i.e.\\\\-a=-1\\\\i.e.\\\\a=1`

Hence,

`b=6\\\\and\\\\c=8`

Hence, the equation of blue parabola is:

`y=x^2+6x+8`

• The red parabola passes through:

(-4,0) , (-3,-1) and (-5,-1)

Hence, the three equations are:

`16a-4b+c=0----------(1)\\\\9a-3b+c=-1----------(2)\\\\25a-5b+c=-1-----------(3)`

on solving the three equations we have:

`a=-1\\\\b=-8\\\\and\\\\c=-16`

Hence, we have the equation of the red parabola as:

`y=-x^2-8x-16`

Hence, the equation of the graph that need to be solved is:

`x^2+6x+8=-x^2-8x-16`