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Daniel [21]
3 years ago
10

Formulate the quadratic function that contains the points (-1,4), (0,2) and (2,4).

Mathematics
2 answers:
igor_vitrenko [27]3 years ago
5 0

Answer:

f(x)=x^2-x+2

Step-by-step explanation:

Quadratic equation form : y=ax^2+bx+c   --1

We are given points :(-1,4), (0,2) and (2,4).

Substitute the point (0,2) in the quadratic equation.

2=a(0)^2+b(0)+c

2=c

Thus the value of c is 2

Substitute the value of c in 1

Thus equation becomes: y=ax^2+bx+2   --2

Now substitute the point (-1,4) in 2

4=a(-1)^2+b(-1)+2

4=a-b+2

a-b=2    ---3

Now substitute point (2,4) in 2

4=a(2)^2+b(2)+2

4=4a+2b+2

2=2a+b+1

2a+b=1   --4

Now solve 3 and 4 to find the value of a and b

Substitute the value of a from 3 in 4

2(2+b)+b=1

4+2b+b=1

4+3b=1

3b=-3

b=-1

Substitute the value of b in 3

a-(-1)=2

a+1=2

a=2-1

a=1

Thus a = 1, b =-1 and c = 2

Substitute the values in 1

y=x^2-x+2

Thus the quadratic function that contains the points (-1,4), (0,2) and (2,4) is   f(x)=y=x^2-x+2

Hence Option 3 is correct.

larisa86 [58]3 years ago
4 0

f(x) = x2 - x + 2

f(-1)=(-1)²-(-1)+2=4   contain the point (-1,4)

f(0) = 0²-0+2 = 2   contain  the point (0,2)

f(2) = 2²-2+2 =4   contain the point (2,4)

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