Question

2.2.30QuesticFind a quadratic function that includes the set of values below.(0,6), (2,8), (3,0)The equation of the parabola is y=0

Answer 1

The form of quadratic is:

`y=ax^2+bx+c`

Since (0,6) is given, we know c = 6, thus we have:

`\begin{gathered} y=ax^2+bx+c \\ ax^2+bx+6 \end{gathered}`

Point 2 is (2,8), replace x and y and find equation:

`\begin{gathered} y=ax^2+bx+6 \\ 8=a(2)^2+b(2)+6 \\ 8-6=4a+2b \\ 4a+2b=2 \end{gathered}`

Putting point 2 (3,0), we have:

`\begin{gathered} y=ax^2+bx+6 \\ 0=a(3)^2+b(3)+6 \\ 9a+3b=-6 \end{gathered}`

Solving the 2 simulatenous equations for a and b, we get:

a = -3

b = 7

Now u have all the values, a, b, and c.

Just put it in the general form of parabola :

`y=-3x^2+7x+6`

y = -3x^2 + 7x + 6