Question

Write the quadratic function in vertex form. y = x2 - 2x + 5

Answer 1

Answer:

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

Step-by-step explanation:

To write this quadratic function in vertex form, which is the explicit form of the parabola, we have to complete the square in the expression.

First, we have to take the coefficient of the linear term and find the squared power of its half:

$(\frac{b}{2} )^{2}=(\frac{2}{2} )^{2}=1$

Then, we add and subtract this number in the quadratic expression:

$y=x^{2}-2x+5+1-1$

Now, we use the three terms that can be factorize as the squared power of a binomial expression:

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

Then, we find the square root of the first term and third term, and we form the squared power:

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

Now, this vertex form is explicit, because it says from the beginning what's the coordinates of the vertex, which is: $(1;4)$, as minimum, because the parabola is concave up.

Answer 2

Vertex form formula: y = a(x-h)^2 +k, with vertex (h,k)
There are multiple ways to find the vertex. One way is to find the roots and then find the x value exactly in between them, because this parabola is symmetrical. 

0 = (x - 3)(x + 2), so x = 3 and -2. The point directly in the middle is x = 1/2 = h 

To find the y value of the vertex, plug in 1/2 to the equation.

(1/2)^2 - 2(1/2) + 5 = 4.25 = k

y = (x - 0.5)^2 + 4.25