the curve y=ax^2 + bx passes through (2,0) and (4,8). find a and b.

Question

the curve y=ax^2 + bx passes through (2,0) and (4,8). find a and b.

Answer 1

y=ax² + bx

 

Plug in the two given points, (2,0) and (4,8):

 

0 = a2² + b2 = 4a + 2b

8 = a4² + b4 = 16a + 4b

 

4a + 2b = 0

16a + 4b = 8    (you can reduce this one to 2a + b = 2 by dividing both sides by 4)

 

Can you solve the system of linear equations to find a and b?  You can use either the substitution or elimination method.