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.

justaguide | Certified Educator

We are given that the points (1,2) and (0, 3) are on the graph of f(x)=ax^2+x+c.

We can write the following equations:

3 = a*0 + 0 + c = c

and  2 = a +1 +c = a + c + 1

Now from the first equation we have c = 3.

Substitute this in 2 = a +1 +c

=> 2 = a + 1 + 3

=> a = -2

Therefore the real numbers a and c are a = -2 and c = 3.

neela | Student

To 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.

(1,2) is on ax^2+x+c.

=> f(1) = a*1^2+1+c = 2.

Or a+1+c = 2

a+c = 2-1= 1.

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

(0,3) is on ax^2+x+c.

=> f(0) = a*0^2+0+c = 3.

=> c = 3....(2)

We put c = 3 in (1): a+c = 1. Or a+3 = 1. So a = 1-3 = -2.

Therefore a = -2, c = 3.

So ax^2+x+c = -2x^2+x+3.

giorgiana1976 | Student

If the graph of the function f(x) is passing through the given points, then the coordinates of these points have to 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