Determine the real numbers Determine the real numbers a c if

Determine the real numbers

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

Solution

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