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

Complete The Square To Findthe Vertex Of This Parabolax 2x Y 4 0 class=

Sagot :

Given:

[tex]x^2-2x+y-4=0[/tex]

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:

[tex]y=-x^2+2x+4[/tex]

Now, take the vertex form of a parabola:

[tex]y=a(x-h)^2+k[/tex]

Apply the standard form of a parabola:

[tex]\begin{gathered} ax^2+bx+c \\ \\ -x^2+2x+4 \end{gathered}[/tex]

Thus, we have:

a = -1

b = 2

c = 4

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

[tex]\begin{gathered} h=-\frac{b}{2a} \\ \\ h=-\frac{2}{2(-1)} \\ \\ h=-\frac{2}{-2} \\ \\ h=1 \end{gathered}[/tex]

To find the value of k, we have:

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

We have the values:

h = 1

k = 5

The vertex of the parabola is:

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

ANSWER:

(1, 5)