Answer:
The quadratic function that passes through given points is y = 2 x² - x + 3 .
Step-by-step explanation:
The given quadratic function as
y = a x² + b x + c
The equation passes through the points ( - 1 , 6 ) , ( 1 , 4 ) and ( 2, 9 )
As The points passes through equation then
At points ( - 1 , 6 )
6 = a (1)² + b ×( - 1 ) + c
Or, a - b + c = 6 .....A
Again At points ( 1 , 4 )
4 = a (1)² + b × 1 + c
Or, a + b + c = 4 .......B
Similarly At points ( 2 , 9 )
9 = a (2)² + b × 2 + c
Or, 4 a +2 b + c = 9 ....,,,C
Now solving equation A and B
( a - b + c ) + ( a + b + c ) = 6 + 4
Or, a + c = [tex]\frac{10}{2}[/tex]
I.e a + c = 5 ......D
Similarly Solving equation B and C
( 4 a +2 b + c ) - 2 × ( a + b + c ) = 9 - 2 × 4
Or, ( 4 a - 2 a + 2 b - 2 b + c - 2 c ) = 9 - 8
Or, ( 2 a - c ) = 1 .....E
Solving D and E
( a + c ) + ( 2 a - c ) = 5 + 1
Or, 3 a = 6
∴ a = [tex]\frac{6}{3}[/tex]
I.e a = 2
Put the value of a in Eq D
So , a + c = 5
Or, c = 5 - a
∴ c = 5 - 2 = 3
I.e c = 3
Put The value of a and c in Eq A
a - b + c = 6
Or, b = a + c - 6
Or . b = 2 + 3 - 6
∴ , b = 5 - 6
I.e b = - 1
Now, Putting the values of a , b , c in the given quadratic equation
I.e y = a x² + b x + c
Or, y = 2 x² + ( - 1 ) x + 3
∴ The quadratic eq is y = 2 x² - x + 3
Hence The quadratic function that passes through given points is y = 2 x² - x + 3 . Answer
