Question

write the function in vertex form. identify the vertex.
y = 2x^2 - 4x + 5​

Answer 1

Answer:

$\large\boxed{f(x)=2(x-1)^2+3}$

Step-by-step explanation:

The vertex form of a quadratic function f(x) = ax² + bx + c:

$f(x)=a(x-h)^2+k$

Where (h, k) is a vertex.

$h=\dfrac{-b}{2a},\ k=f(h)$

We have:

$f(x)=2x^2-4x+5\to a=2,\ b=-4,\ c=5$

Calculate h and k:

$h=\dfrac{-(-4)}{2(2)}=\dfrac{4}{4}=1\\\\k=f(1)\to k=2(1^2)-4(1)+5=2-4+5=3$

Finally:

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