How does -b/2a output either the highest, or lowest point in a parabola? Like how does it work? I know the purpose of the formula, but I don't understand how applying it GIVES you the highest or lowest. It's been on my mind since English class, I love math but I can't figure out how that formula works...
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I assume you know the whole quadratic formula or can look it up.
Here it is simplified: [-b + or - D]/2a
OR -b/2a + d and -b/2a - d
On a number line, what is the midpoint of 7+3 and 7-3? I bet you see that as 7 pretty quickly.
Same for the quadratic formula: the middle of the two answers is -b/2a
parabolas are symmetric. so the middle point is the lowest if the parabola opens up like a "U" or the highest if it opens down.
Hope that helps.
Here it is simplified: [-b + or - D]/2a
OR -b/2a + d and -b/2a - d
On a number line, what is the midpoint of 7+3 and 7-3? I bet you see that as 7 pretty quickly.
Same for the quadratic formula: the middle of the two answers is -b/2a
parabolas are symmetric. so the middle point is the lowest if the parabola opens up like a "U" or the highest if it opens down.
Hope that helps.
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Well, you could easily do it with basic calculus.
But it is also the average of the roots (in the imaginary), and it kinda makes sense that the average will be special. If you write out the two roots, with the quadratic equation, and take their average, you will get -b/2a.
But it is also the average of the roots (in the imaginary), and it kinda makes sense that the average will be special. If you write out the two roots, with the quadratic equation, and take their average, you will get -b/2a.
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y = ax^2+bx+c
dy/dx = 2ax+b = 0 for maximum or minimum
2ax = - b
x = -b/2a
dy/dx = 2ax+b = 0 for maximum or minimum
2ax = - b
x = -b/2a
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y = ax² + bx + c
dy/dx = 2ax + b
At the vertex, dy/dx = 0.
2ax + b = 0
2ax = -b
x = -b/(2a)
dy/dx = 2ax + b
At the vertex, dy/dx = 0.
2ax + b = 0
2ax = -b
x = -b/(2a)