Determine the parabola that passes through the points (1,−2), (2,3), and (3,10) If the parabola also passes through (5,k) what is k?

Answer 1

(1,−2), (2,3), and (3,10)

The system is three equations

from

y=ax²+bx+c

a+b+c=-2

4a+2b+c=3

9a+3b+c=10

subtracting first from second two

3a+b=5

8a+2b=12

then easy to find a=1

a=1, b=2, c=-5

parabola is

y=x²+2x-5

when x=5, k=y=25+10-5=30

Answer 2

10 = a(3)² + b(3) + c

3 = a(2)² + b(2) + c

Can you solve the system?

When you have the equation substitute 5 for x and calculate k.