Finding the turning point of a parabola

Question

I know how to find the turning point of a parabola in most equations but I'm not sure how to solve it in this form, if anyone can help me please do! $$y=x^2+4x-5$$ Thanks

Answer 1

We have

$$x^2 + 4x - 5 = (x^2 + 4x + 4) - 4 - 5 = (x + 2)^2 - 9.$$

Therefore, the vertex is at $(-2, \, -9)$.

Answer 2

The vertex can be found by plugging $x$ with $-\frac {b}{2a}$ give the form $ax^2+bx+c=0$.

So with your example $x^2+4x-5=0$, we have $$a=1\\b=4\\c=-5\tag{1}$$ So $-\frac {b}{2a}=-\frac {4}{2}=-2$. Plugging that into the quadratic gives $$f(-2)=4-8-5=-9\tag{2}$$ Therefore, the vertex is $(-2,-9)$.