Question

Given ​ f(x) = x^2 − 2x − 5​.

Answer 1

Answer:

$(x - 1)^2 - 6$

Step-by-step explanation:

You need to know:

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

The vertex is at

(h, k)

Need to know about perfect squares

Need to know how to complete the square.

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To convert $x^2-2x-5$ you need to complete the square on the equation.

Complete the Square $x^2 - 2x -5$

$x^2 - 2x -5$

$(x^2 - 2x) -5$

Divide -2 by 2 and then square it.

$\frac{-2}{2} = -1$

$-1^2 = 1$

Add the one to the parentheses and subtract the one from the 5

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

Square  $(x^2 - 2x +1)$

$(x-1)^2$

Now we have

$(x - 1)^2 -5 -1$

Next add -5 - 1 = -6

$(x - 1)^2 - 6$

Our quadratic is in vertex form now.

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

our equation =  $(x - 1)^2 - 6$

Vertex = (1, -6)