Question

Need help with algebra 2 Question:
Write an equation for the quadratic function
(1,5)(2,8)(3,9)(4,8)

Answer 1

So a quadratic equation is an equation or order 2. This means you will have an x^2 term:

$$
y=ax^2+bx+c
$$
We need to find a,b and c.
We will use the 3 points to generate 3 equations.
With 3 equations and 3 unknowns (a,b and c) we can solve.
Using the first point (1,5) we have x=1 and y=5
$$
5=a1^2+b\cdot 1+c=a+b+c
$$
Now do this for the next two points to find the other two equations.

Can you do this?

Answer 2

\[8=a2^2+b \times 2+c=a+b+c\]

Answer 3

\[9=a3^2+b \times 3+ c = a+b+c\]

Answer 4

$$
8=a2^2+b \times 2+c=4a+2b+c\\
9=a3^2+b \times 3+ c = 9a+3b+c
$$
So now you have 3 equations:
$$
5=a+b+c\\
8=4a+2b+c\\
9=9a+3b+c
$$
You can solve for a,b and c to get your answer:
$$
y=ax^2+bx+c
$$
The last point (4,8) is redundant because you only need 3 points to perfectly fit a quadratic equation. Three points is sufficient because you have three unknowns, a, b and c.