Question

Create the quadratic function that contains the points (0,2), (1,0), and (3,10). Show all of your work for full credit.

Answer 1

Answer:

y=7/3x²-13/3x+2

Step-by-step explanation:

Determine the value of c:

y=ax²+bx+c

2=a(0)²+b(0)+c

2=c

Substitute (1,0) into the quadratic and create an equation with a and b:

y=ax²+bx+2

0=a(1)²+b(1)+2

0=a+b+2

-2=a+b

Do the same with (3,10) to get a second equation:

y=ax²+bx+2

10=a(3)²+b(3)+2

10=9a+3b+2

8=9a+3b

Set the two equations equal to each other and solve for a and b:

-2=a+b

8=9a+3b

Multiply first equation by 3 and eliminate b to find a:

 -6=3a+3b

- (8=9a+3b)

_______

-14=-6a

14/6=a

7/3=a

Substitute 7/3=a into the first equation:

-2=7/3+b

-2-(7/3)=b

-13/3=b

Final equation:

y=7/3x²-13/3x+2

See the graph for a visual representation