Question

How can I find the vertex, axis of symmetry? I know to find x and y intercepts i use the quadratic formula.

I am given the parabola y=x^2+6x+5

I do not want the answer.. Just please explain to me how to solve for it. what method do I use???

Answer 1

A parabola which opens up has a lowest point and a parabola which opens down has a highest point.

The highest or lowest point on a parabola is called the vertex.

This point, where the parabola changes direction, is called the "vertex".


To determine the vertex of the graph of a quadratic function:

f(x) = a x ^ 2+ b x + c

we can either:

1) Use the method of completing the square to rewrite the function in the form:

f(x) = a ( x - h ) ^ 2 + k

The vertex poit is a point with coordinates: (h, k)

x coordinates of the vertex = h

y coordinates of the vertex = k


OR


2) Use the formula:

x coordinates of the vertex = - b / 2a

y coordinates of the vertex = f ( x ) = c - b ^ 2 / 4a



The axis of symmetry is a vertical line through the vertex.

The equation of the axis of symmetry is the equation of the vertical line passing through x and y coordinate of the vertex:

The equation of the axis of symmetry:

x = x coordinate of the vertex

For each value of y

x = - b / 2a

Answer 2

y coordinates of the vertex = f ( x ) = f ( x = - b / 2a ) = c - b ^ 2 / 4a