Parabola Question (1 Viewer)

[dionb2014]

In the standard form of a quadratic relationship y=ax^2+bx+c what do the a, b and c represent about the parabola. I know that the c value tells us the y intercept of the parabola. The a value tells is how wide the parabola is and if it is concave up or down. But what does the B value represent or is there anything I am missing.
Thanks

 

[Aerath]

'b' doesn't really represent anything.

 

[khfreakau]

lol in yr11/12 maths this form is only used to solve quadratic equations, you would never use it to infer information about the graph.
if you wanted to find out more about the importance of these values, you would complete the square. in of which case you would find out that b/2a = the x coordinates of the vertex. note that b/a is the sum of the roots, so b/2a is the sum of roots on two. hence you're simply finding the average value between the two roots when you find b/2a, and this allows you to find the vertex.

 

[dionb2014]

So you find the average of each of the + and - quadratic formulas to get b/2a?

 

[jamesfirst]

The reason why 'c' is the y-intercept is not because it's the 'c'...

If you let x=0, you get y=c. that's why. Soo... the a b c really has no significance except when used in the quadratic formula or the vertex formula.

 

[khfreakau]

So you find the average of each of the + and - quadratic formulas to get b/2a?

in a way yes, but you can simply use the coefficients and sum/products of roots to deduce that.