About quadratic functions , need help in it .?

Question

I had a lecture about quadratic functions , then while reading the lecture papers i could see that we may get the value of x by this equation = x= - b/2a .. and y < m> by this equation - d/4a ... then i found this writen in the lecture papers that the vertex of the quadratic function may be considered as following ( -b/2a , d/4a ) the y or m wasnt followed by a negative mark , so which is right .. should it be followed by a negative mark or no ......... ?

Answer 1

Quadratic Equations represents a Parabola in a graph. A Parabola is a U shaped figure which curves at point and continue in other direction. This point is known as Vertex.

So x= - b/2a and y = -d/4a are the points in the parabola at any a and b..

while the vertex is the point at which the parabola takes a curve..

Answer 2

quadratic equation is y = ax^2 +bx +c = 0
x = -b/2a is the axis of symmetry of the parabola.
The vertex lies on the axis of symmetry. Thus if you plug
x=-b/2a into the quadratic equation you get
y = a(-b/2a)^2 +b(-b/2a) +c = b^2/4a -b^2/2a +c
y = -b^2/4a +c = -(b^2-4ac)/4a = -d/4a where d is the Discriminant.
So the vertex is at (-b/2a, -d/4a) [d= b^2-4ac]
The slope m = 2ax+b at any point x on the parabola.

Answer 3

The vertex is -b/2a
quadratic formula
x = -b +-sqrt(b^2-4ac)
-----------------------
2a

y value, put your x value in, and solve for y