Question

Determine the equation of quadratic function represented by the table of value below.

Answer 1

A

Explanation:

The general rule for the quadratic function is

`y=ax^2+bx+c`

Use the data from the table:

`y(0)=6\Rightarrow 6=a\cdot 0^2+b\cdot 0+c\\ \\y(1)=4\Rightarrow 4=a\cdot 1^2+b\cdot 1+c\\ \\y(-1)=10\Rightarrow 10=a\cdot (-1)^2+b\cdot (-1)+c`

We get the system of three equations:

`\left\{\begin{array}{l}c=6\\ \\a+b+c=4\\ \\a-b+c=10\end{array}\right.`

From the first equation

`c=6,` then

`\left\{\begin{array}{l}a+b=-2\\ \\a-b=4\end{array}\right.`

Add these two equations:

`a+b+a-b=-2+4\\ \\2a=2\\ \\a=1`

So,

`b=-2-a=-2-1=-3`

The quadratic function is

`y=1\cdot x^2-3x+6\\ \\y=x^2-3x+6`