the curve y=ax^2+bx+c passes through the points (1,4) (-2,19) (0,5) find the equation of the curve
Answers
Step-by-step explanation:
2x^2+x-y+5=0
this is the equation of curve
Answer:
How do I find the equation of a curve y=ax^2+bx+c that passes through (1,8), (-1,2) and (2,14)?
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How do I find the equation of a curve y=ax^2+bx+c that passes through (1,8), (-1, 2) and (2,14)?
x=1,y=8
means that
8=a(1)2+b(1)+c.
Label this as equation (1):
8=a+b+c……(1).
x=−1,y=2
means that
2=a(−1)2+b(−1)+c.
This simplifies to equation (2):
2=a−b+c……(2)
x=2,y=14
means that
14=a(2)2+b(2)+c.
This is simplified to get equation (3):
14=4a+2b+c……(3)
Add equation (1) and equation (2) to eliminate b and get
2a+2c=10.
Divide this by 2 and obtain the next equation, that is, equation (4):
a+c=5……(4).
Add 2 times equation (2) to equation (3) to eliminate b again and get
6a+3c=18.
Divide this through by 3 and get equation (5):
2a+c=6……(5)
Subtract equation (4) from equation (5) to eliminate c and get
a=1.
Then substitute this into equation (4) and get
1+c=5
so that
c=4.
Go back to equation (1) and replace a and c by these results and get that
1+b+4=8,
from which
b=3.
∴y=x2+3x+4
is the equation of the parabola containing the three given points
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