Why is the vertex formula -b/2a, - discriminent/4a. What the meaning being it

Favorites|Homepage
Subscriptions | sitemap

HOME > > Why is the vertex formula -b/2a, - discriminent/4a. What the meaning being it

Why is the vertex formula -b/2a, - discriminent/4a. What the meaning being it

[From: ] [author: ] [Date: 13-05-04] [Hit: ]

and the parabola, having a vertex with negative y, will also have two x-intercepts, corresponding to the real roots.If the discriminant is I hope this demystifies the question for you.-The vertex form of parabola is y = a(x - h)^2 + k where the vertex is at (h,......

Well, if the discriminant = 0, the equation has a double root. That corresponds to the parabola having the vertex on the origin.

If the discriminant is > 0, the equation has two real roots, and the parabola, having a vertex with negative y, will also have two x-intercepts, corresponding to the real roots.

If the discriminant is < 0, the equation has two complex non-real roots. And the parabola, having a vertex with positive y, has no x-intercepts, corresponding to "no real roots."

I hope this demystifies the question for you.

-

The vertex form of parabola is y = a(x - h)^2 + k where the vertex is at (h,k)

y = ax^2 + bx + c
=> y - c = ax^2 + bx
=> (y - c)/a = x^2 + (b/a)x
=> (y - c)/a + (b/2a)^2 = x^2 + (b/a)x + (b/2a)^2
=> (y - c)/a + b^2/4a^2 = (x + b/2a)^2
=> (y - c)/a = (x + b/2a)^2 - b^2/4a^2
=> y - c = a(x + b/2a)^2 - b^2/4a
=> y = a(x + b/2a)^2 + c - b^2/4a
=> y = a(x + b/2a)^2 + (4ac - b^2)/4a

so h = - b/2a and k = (4ac - b^2)/4a

12

keywords: discriminent,being,meaning,vertex,is,Why,formula,it,What,the,Why is the vertex formula -b/2a, - discriminent/4a. What the meaning being it