Find equation of parabola, given three points

Question

(0,4) (1,3) (2,6)

I know I have to use the equation for a parabola whose axis of symmetry is vertical:

y = ax^2 +bx + c

The first step is to plug the points into an equation:

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

4= a+c This is where I get confused. My book says C=4?

3= a(1)^2 + b(1) +c

3= a +b +c This is more confusing, book says a+b= -1 ??

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

6= 4a+2b+c This comes to 2a +b =1 ????

Can anyone explain how the answers from each equation were derived? Still confused.

Answer 1

Hello Brian,

After you plug in x = 0, you get a(0²) + b(0) + c.

What is 0²? It is 0 not 1.

So it is 4 = c not 4 = a + c.

Further down, you are right that 3 = a + b + c !

Now we know that c = 4 so substitute that in.

3 = a + b + 4.

What do you get after that?

Further down,

you wrote 6 = 4a + 2b + c which is right!

Then plug in c = 4.

6 = 4a + 2b + 4

Subtract 4 from both sides to get 2 = 4a + 2b.

Then how do they get 2a + b = 1?