# Determine the real numbersDetermine the real numbers a, c if the points (1;2) and (0;3) are on the graph of f(x)=ax^2+x+c.

justaguide | College Teacher | (Level 2) Distinguished Educator

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The points (1 , 2) and (0,3) lie on the graph of the function f(x) = ax^2 + x + c.

This gives two equations:

2 = a*1 + 1 + c ...(1)

3 = 0 + 0 + c ...(2)

From (2) we get c = 3

substitute in (1)

2 = a + 1 + 3

=> a = -2

The values of a and c are -2 and 3 respectively.

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Since the graph of the function f(x) is passing through the given points, then the coordinates of these points must verify the expression of the function.

The point A(1 , 2) is on the graph if and only if:

f(1) = 2

We'll substitute x by 1:

f(1) = a + 1 + c

a + 1 + c = 2

The point B(0 , 3) is on the graph if and only if:

f(0) = 3

We'll substitute x by 0:

f(0) = c

c = 3

We'll substitute c = 3 in:

a + 1 + c = 2

a + 1 + 3 = 2

We'll subtract 4 both sides:

a = 2 - 4

a = -2

The expression of f(x) is: f(x) = -2x^2 + x + 3