Question

Convert the given form of the function into the two other forms.

Vertex form -> y - 5 = -2(x+1)^2
I think standard would be -> y=-2x^2-4x+3
Can anyone explain to me how you get intercept form?

Info you might need:
Standard form = y = ax^2 + bx + c
Vertex form = y = a(x-h)^2
Intercept form = y = a(x-r1)(x-r2)

Answer 1

set y = 0 and solve for x
you will get
\[0-5=-2(x+1)^2\]
\[(x+1)^2=\frac{5}{2}\]
\[x+1=\pm\sqrt{\frac{5}{2}}=\pm\frac{\sqrt{10}}{2}\]
\[x=-1-\frac{\sqrt{10}}{2},x=-1+\frac{\sqrt{10}}{2}\]

Answer 2

so in factored form you will get
\[y=2(x+1+\frac{\sqrt{10}}{2})(x+1-\frac{\sqrt{10}}{2})\]