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<u>Answer:</u>
The quadratic function passing through the points (0,-3), (1,2), and (2,-1) is
<u>Solution: </u>
Given that required function is quadratic
And function is passing through points (0 , -3) , (1 , 2) and (2 , -1)
General form of a quadratic function is ----(A)
f(x) is nothing but output value that is y.
That is f(x) = y
So --- (1)
Let’s use equation (1) to get required function.
Given that function passes through (0 , -3) means when x = 0 , y = -3
On substituting value of x and y in equation (1) we get
-3 = 0 + 0 + c
c = -3
On substituting value of c in equation (1) we get
---(2)
Function also passes through point (1, 2) that is at x = 1 , y = 2.
On substituting value of x and y in equation (2) we get
2 = a + b – 3
a + b = 5
b = 5 - a -------(3)
Also given function passes through point ( 2 , -1) means when x = 2 , y = -1
On substituting value of x and y in equation (2) we get
-1 = 4a + 2b – 3
4a + 2b = 2
2a + b = 1 ------- (4)
On substituting value of b from equation (3) in equation (4), we get
2a + (5 - a ) = 1
a + 5 = 1
a = 1-5 = -4
From equation (3) b = 5 – a = 5 – (-4) = 9
b = 9
Now we have a = -4, b = 9 and c = -3
On substituting calculated values of a, b, and c in equation (A) we get
Hence required quadratic function is