Question

The points (0,5), (1,6), (2,9), and (3,14) are on the graph of a function. Write an equation in standard form that represents the function

Answer 1

4 points belong to a function

Then

f(0) = 5

f(1) = 6

f(2) = 9

f(3)= 14

y = f(x) = ax^2 + bx + c

(x,y) = (0,5) means c= 5

Now rest to find a,b

(x,y) = (1,6) ,. Then. a•1^2+ b•1 = a + b= 1

Now

(x,y)= (2,9). Then a•2^2 + b•2 + 5 = 9

. Then. 4a + 2b = 4

(x,y) = (3,14). Then. a•3^2 + b•3 = 9

. So. 9a + 3b = 9

Now find a, b

b = 1 - a

Then

2a + (1 - a) = 2

2a - a = 2 - 1

a = 1

Also

b = 1 - a = 1 -1 = 0

THEN a,b,c are

a= 1

b= 0

c= 5

and ANSWER IS

equation f(x)

f(x) = 1•x^2 + 0•x + 5

f(x) = x^2 + 5