Slope of a function

[Farid Khan]

Is the slope of a quadratic function at its vertex is always 0. If so, can u  please tell me why?

[Anand Iyer]

Yes, the slope is 0, at the vertex.

It's always parallel to X-axis.

Try this out in any of the online tools geogebra/desmos.  

Now, I'm not sure how to prove it mathematically though...

[Vijender Singh]

Perhaps...try this...

at vertex, x = -3,  

 

Slope = 2ax + b => 2*1*-3 + 6 => -6 + 6 = 0......(a = 1 and b = 6)

Regards,

Vijender

On Wednesday, November 18, 2020 at 5:03:41 PM UTC+5:30 Farid Khan wrote:

[Malabika Guha Mustafi]

@ Anand, if the equation is in ay^2 + bx+c form? Is it still parallel to x axis?

When y= ax^2 + bx +c

then slope of vertex is parallel to x axis.

when x=ay^2 +by +c

then slope is parallel to y axis so undefined.

[Anand Iyer]

ah, you got me!  

you're right about the quadratic functions in y, slope through vertex is undefined...

[Malabika Guha Mustafi]

@ Farid Khan, in brief

slope is 0 when a parabola is up open and down open and slope is parallel to x axis.

slope is undefined when parabola is right open or left open and slope is parallel to y-axis.

Here, we are considering the slope of vertex.

[Farid Khan]

Thanks for clarifying my doubt guys. Really appreciate it!!

[nikhil kambli]

sideways parabola i.e rt or left opening parabola is not a function .?

[Malabika Guha Mustafi]

If it is defined  positive or negative. Then other wise no

[nikhil kambli]

I didn't understand

[Malabika Guha Mustafi]

If it is specified as right open or left open then it is function otherwise not. Then, we can not decide between two values of root. It is explained in one tutorial.

[Debajyoti Biswas]

@Malabika, Very nice answer!

[Malabika Guha Mustafi]

Thank you

[Malabika Guha Mustafi]

@nikhil kambli  week 4  .Tutorial 7