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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
