Question

What is the value of a for the quadratic function represented in thefollowing table?

Answer 1

The value of a is;

`a=5`

Step-by-step explanation:

Given a quadratic equation;

`y=ax^2+bx+c`

The values of x and y are given in the table.

to get the value of c,

at x =0, y=2.

let us substitute into the equation;

`\begin{gathered} y=ax^2+bx+c \\ 2=a(0)^2+b(0)+c \\ 2=c \\ c=2 \end{gathered}`

Since, we have the value of c. the equation becomes;

`y=ax^2+bx+2`

let us proceed to find a and b.

at x=-1, y=16

also at x=1,y=-2

let us substitute the two values;

`\begin{gathered} atx=-1,y=16 \\ y=ax^2+bx+2 \\ 16=a(-1)^2+b(-1)+2 \\ 16=a-b+2 \\ a-b=16-2 \\ a-b=14\text{ -------1} \\ at\text{ x=1, y=-2} \\ y=ax^2+bx+2 \\ -2=a(1)^2+b(1)+2 \\ -2=a+b+2 \\ a+b=-2-2 \\ a+b=-4\text{ ------2} \end{gathered}`

To get a add equation 1 and 2 together;

`\begin{gathered} a-b+a+b=14-4 \\ a+a-b+b=10 \\ 2a=10 \\ a=(10)/(2) \\ a=5 \end{gathered}`

Therefore, the value of a is;

`a=5`