Understanding what you're doing.

[streetmeat]

How important is it to you to understand the math your applying? I am decent at math when it comes to remembering rules and applying everything systematically, and i do well at solving problems using the tools i am given, but sometimes i have trouble understanding exactly why certain rules work down to a science, which kind of bothers me and makes me worry about it affecting my performance later on if i take like an engineering course with intense math.

 

[Werg22]

It's important when you are confronted to a new sort of problem. Understanding the math you are applying allows you to know if what you know can be applied to that problem. From the foundations of your understanding, you will be able to attack the problem from the right angle.

 

[ice109]

it is extremely important

 

[streetmeat]

can someone please explain to me then why h = -b/2a in a quadratic function where f(x) = ax^2 + bx +c = a(x-h)^2 + k

 

[cristo]

can someone please explain to me then why h = -b/2a in a quadratic function where f(x) = ax^2 + bx +c = a(x-h)^2 + k

Huh? That's a bit of a weird change of topic! Expand the brackets and see what you get.

 

[Kummer]

can someone please explain to me then why h = -b/2a in a quadratic function where f(x) = ax^2 + bx +c = a(x-h)^2 + k

Okay, say the parabola,
f(x)=ax^2+bx+c

Intersects the x-axis at points (a,b) and (c,d).

Show the axis of symettry is right in the middle of those two points on the x-axis. Meaning, (a+c)/2

But, "a" and "c" are the two roots (zeros) of f(x). And by Viete's formula the sum of the two roots is (-b/a). So h=(-b/a)/2 = (-b/2a)

 

[symbolipoint]

can someone please explain to me then why h = -b/2a in a quadratic function where f(x) = ax^2 + bx +c = a(x-h)^2 + k

'h' is the value representing horizontal translation. The value is difficult (or impossible - depending on what/how much one knows) to see in general form of the expression; but by completion of the square, and then setting into standard form, you can obtain the value of 'h' directly.

 

[morson]

Yes, always helpful to understand the concept.