Explain the relationship between a parabola's x-intercepts and its vertex ?

Question

 no additional

Answer 1

In vertex form, the equation of a parabola looks like the following:

 

y-k=4p*(x-h)²

 

(h,k) are the coordinates of the vertex, p is the distance from the vertex to the focal point as measured on the axis of symmetry. x=h will be the axis of symmetry.

 

When y=0, the resulting value of x will be the x-intercepts.

 

for the parabola,

 

0-k=4p*(x-h)²

 

-k/4p=(x-h)²  Divide both sides by 4p.

 

+ or - √-k/4p=x-h  Take square root of both sides.

 

h + √-k/4p or h- √-k/4p=x  These two values of x are the x-intercepts.

 

If no solution can be found, then the parabola will not have any x-intercepts (true when vertex has a + y coordinate).

Answer 2

X-intercepts are found when Y=0, use the quadratic equation. The y-intercepts are found when x=0. See the link for examples. 

 

http://www.mathwarehouse.com/geometry/parabola/parabola-intercepts.php