Question

Use the quadratic formula f(x) =2x square -12x+17 to determine the coordinates of the vertex of the best fitting parabola. (h,k)=

Answer 1

Given: A quadratic equation

`f(x)=2x^2-12x+17`

Required: To find the vertex of the given function.

Explanation: For the quadratic equation of the type

`f(x)=ax^2+bx+c`

The vertex is given by,

`V=(-(b)/(2a),f(-(b)/(2a)))`

Hence, the x coordinate of the vertex is

`\begin{gathered} x=-(b)/(2a) \\ =(12)/(2(2)) \\ =3 \end{gathered}`

Now for the y coordinate finding f(x) at x=3

`\begin{gathered} f(3)=2(3^2)-12(3)+17 \\ =-1 \end{gathered}`

The vertex of given parabola is (3,-1).

Final Answer: The vertex is (h,k)=(3,-1)