I would just like a second opinion please to ensure I am doing this correctly.
When y = 0
0 = -x^2 + 4x + 5
- 5 = 4x
x = - 1.25
There're two solutions (if $\displaystyle D\geq0$) for a quadratic equation by using the quadratic formula:
$\displaystyle x_1,x_2=\frac{-b\pm\sqrt{D}}{2a}$
So in this case:
$\displaystyle x_1=\frac{-4+6}{-2}=-1$
$\displaystyle x_2=\frac{-4-6}{-2}=\frac{-10}{-2}=5$
I understand the two roots and how you got them, but the formula has been modified.
- b + or - square root D / 2a
See the changes I have not seen before?
Capital D not squared, and - 4ac missing?
Like I said before this subject is new to me and is a new learning curve.
I don't think the formula has been modified.
In general if you have a quadratic equation:
$\displaystyle ax^2+bx+c=0$
Then this equation has:
two different solutions (or roots) if $\displaystyle D=b^2-4ac>0$
$\displaystyle x_1=\frac{-b+\sqrt{D}}{2a}$
$\displaystyle x_2=\frac{-b-\sqrt{D}}{2a}$
If $\displaystyle D=0$ then the two identical solutions are:
$\displaystyle x_1,x_2=\frac{-b}{2a}$
If $\displaystyle D<0$:
There're no real solutions.
Is this clear? If you need a prove of this then you can ask it.