The formula for a parabels peak, TP ((-b/2a),(-d/4a)), partially examined.
Here you have to try to prove it by using differential calculus.

a) What characterizes the tangent to a parabola in vertex of the parabola?
b) Use the derivative in the vertex to determine toppunktets førstekoordinat.
c) Determine then the second coordinate with the deployment of the first coordinate in the parabola equation.

Question

The formula for a parabels peak, TP ((-b/2a),(-d/4a)), partially examined. 
Here you have to try to prove it by using differential calculus.

a) What characterizes the tangent to a parabola in vertex of the parabola? 
b) Use the derivative in the vertex to determine toppunktets førstekoordinat. 
c) Determine then the second coordinate with the deployment of the first coordinate in the parabola equation.

mathmale · Answer

Resorting to Google Translate, I see that "toppunktets forstekoordinat" probably means "x-coordinate of the vertex," and that we're to determine the y-coordinate of the vertex.  Norwegian language, right?

I'm assuming that Part b) could be re-written as "use the derivative to determine the x-coordinate of the vertex."  @sulle26?

Welcome to OpenStudy!

anonymous · Answer

@mathmale It's Danish. But yeah that's what it somewhat means... I didn't even notice it. Thanks!

mathmale · Answer

The commonest form of the equation of a parabola is

$$y=ax^2 + bx + c$$

If we differentiate this, obtaining (dy/dx), and set the derivative equal to zero, we are in effect (1) finding the x-coordinate of the vertex and (2) finding the critical value of the function, which in turn locates the x-coordinate of the minimum or maximum of this quadratic.

mathmale · Answer

Please evaluate:$$\frac{ d }{ dx }[y=ax^2+bx+c]$$and set the result equal to zero.  solve for x.  Compare your result to the first coordinate of your  TP ((-b/2a),(-d/4a)).

mathmale · Answer

Forgive me, but I'm taking the liberty of fixing up the grammar here:

"The formula for a parabels peak, TP ((-b/2a),(-d/4a)), partially examined"  would be better expressed as "the coordinates of the vertex of a parabola ... " are [ (-b/2a) , f(-b/2a) ].

accessdenied · Answer

I believe from: -d/4a,  "d" refers to the discriminant of the quadratic.  Which checks out okay.

If you evaluated  y = ax^2 + bx + c  for  x= -b/2a,  you eventually find that (-b^2 + 4ac)/4a is the y-value, where the discriminant is just b^2 - 4ac.

anonymous · Answer

@mathmale, @AccessDenied - I'll try it, i'll tag you if i get stuck, if that's okay! Thank you, though :)