Question

Find the vertex of the quadratic polynomial, f(x) = 4x² -8x + 6

Answer 1

I think its -128x + 6

Explanation:

Answer 2

The equation of a parabola with vertex (h,k) is given by:

`y=a(x-h)^2+k`

Starting from the given equation, complete the square to write the function in vertex form:

`\begin{gathered} f(x)=4x^2-8x+6 \\ =4(x^2-2x)+6 \\ =4(x^2-2x+1-1)+6 \\ =4(x^2-2x+1)+4(-1)+6 \\ =4(x-1)^2-4+6 \\ =4(x-1)^2+2 \end{gathered}`

By comparing that equation with the vertex form of a parabola, we can see that h=1 and k=2.

Therefore, the vertex of the given quadratic polynomial, is:

`(1,2)`