Question

Y=x2-2x-5 Change to vertex form

Answer 1

The vertex form is $y=(x-1)^{2} -6$

Step-by-step explanation:

The given equation $y=x^{2} -2x-5$ is a parabola. The vertex of the parabola is of the form $y=ax^{2} +bx+c$  

The parameters of the parabola are $a=1, b=-2$ and $c=-5$

The vertex of the x-coordinate is given by $x=\frac{-b}{2a}$

Thus, substituting the values of a and b in $x=\frac{-b}{2a}$, we get,

$\begin{aligned}x &=\frac{-(-2)}{2(1)} \\&=\frac{2}{2} \\x &=1\end{aligned}$

Now, substituting $x=1$ in $y=x^{2} -2x-5$, we get,

$\begin{aligned}y &=1^{2}-2(1)-5 \\&=1-2-5 \\y &=-6\end{aligned}$

Thus, the vertex is $(1,-6)$

The equation of parabola to be in vertex form is $y=a(x-h)^{2} +k$

where a is the coefficient of $x^{2}$, h is vertex of the x-coordinate and k is the vertex of the y-coordinate.

Hence, $a=1, h=1$ and $k=-6$

Thus, substituting the values in the equation of the vertex form,

$y=1(x-1)^{2} -6\\y=(x-1)^{2} -6$

Hence, the vertex form is $y=(x-1)^{2} -6$