Question

What is the vertex form of y=-2x2+4x + 3?

Answer 1

Answer:

$y=-2(x-1)^2+5$

Step-by-step explanation:

we have

$y=-2x^2+4x+3$

This is the equation of a vertical parabola open downward

The vertex represent a maximum

Convert the quadratic equation into vertex form

step 1

Factor -2

$y=-2(x^2-2x)+3$

step 2

Complete the square

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

$y=-2(x^2-2x+1)+5$

step 3

Rewrite as perfect squares

$y=-2(x-1)^2+5$ ----> equation in vertex form

The vertex is the point (1,5)