Question

For the function y = -2x2 + 4x + 1, what are the coordinates of the vertex?

Answer 1

Answer:

(1,3)

Step-by-step explanation:

The given function is

$y = - 2 {x}^{2} + 4x + 1$

Factor 2 from the first two terms

$y = - 2( {x}^{2} - 2x) + 1$

Add and subtract the square of half the coefficient of x.

$y = - 2( {x}^{2} - 2x + 1 - 1) + 1$

Let us create perfect square trinomial

$y = - 2( {x}^{2} - 2x + 1 ) + - 2 \times - 1 + 1$

This implies that:

$y = - 2( {x - 1)}^{2}+ 3$

Therefore the vertex is (1,3).

We got this by comparing to

$y = a( {x - h)}^{2} + k$