Question

can you please check my work?

7. Find the equation of the parabola y=ax2+bx+c that passes through the points(0,6),(-2,2), and(3,9/2).

y=ax2+bx+c

6=a(0)2+b(0)+c
2=a(-2)2+b(-2)+c
9/2=a(3)2+b(3)+c
6=c

2=4a+(-2b)+6
9/2=9a+3b+6
-4=4a-2b
-3/2=9a+3b
a=-1/2, b=1

y=(-1/2x)-x+6

Answer 1

your values for a,b,c are correct. However, your final answer is wrong, as you could have verified had you tried to check your answer.

y = -1/2 x^2 + x + 6