Question

Complete the square to findthe vertex of this parabola.x² - 2x + y - 4 = 0([?], [ ])

Answer 1

Given:

`x^2-2x+y-4=0`

Let's complete the square to find the vertex of the parabola.

To solve first move all terms not containing y to the right side of the equation:

`y=-x^2+2x+4`

Now, take the vertex form of a parabola:

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

Apply the standard form of a parabola:

`\begin{gathered} ax^2+bx+c \\ \\ -x^2+2x+4 \end{gathered}`

Thus, we have:

a = -1

b = 2

c = 4

Now, to find the value of h, we have:

`\begin{gathered} h=-(b)/(2a) \\ \\ h=-(2)/(2(-1)) \\ \\ h=-(2)/(-2) \\ \\ h=1 \end{gathered}`

To find the value of k, we have:

`\begin{gathered} k=c-(b^2)/(4a) \\ \\ k=4-(2^2)/(4(-1)) \\ \\ k=4-(4)/(-4) \\ \\ k=4+1 \\ \\ k=5 \end{gathered}`

We have the values:

h = 1

k = 5

The vertex of the parabola is:

(h, k) ==> (1, 5)

ANSWER:

(1, 5)