Derivation for finding vertex and turning point of

Sanai Huerta

Sanai Huerta

Answered question

2022-03-25

Derivation for finding vertex and turning point of parabola?
Form the equation of parabola.
y+D4a=a(x+b2a)2
So , to find vertex of turning point ,
Make y=0 and x=0.
You get b2a and D4a but aren’t we getting these values in +?

Answer & Explanation

lernarfnincln6g

lernarfnincln6g

Beginner2022-03-26Added 14 answers

It is easier to understand it if we substitute variables.
Let: p=y+D4a
s=x+b2a
Then the equation transforms to
p=as2
Where is the vertex of this parabola? Obviously at p=0,s=0.
Vertex at p=0 means it is at y+D4a=0, which means y=D4a
Vertex at s=0 means it is at x+b2a=0, which means x=b2a.
anghoelv1lw

anghoelv1lw

Beginner2022-03-27Added 19 answers

To find the vertex of a parabola, equate the slope to 0. that is dydx=0.
dydx=2a(x+b2a)
so 2a(x+b2a)=0
so x=b2a
Putting the point in the equation, we get the y coordinates as D4a.

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