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- What is -b 2a? : r learnmath - Reddit
The midpoint between the two points lies on axis of symmetry of the graph, so it will have x-coordinate that matches the x-coordinate of the vertex of the parabola, which is x = -b 2a This is the reason that the quadratic formula for the solutions gives x = -b 2a ± something
- Proof of -b 2a - Math Help Forum
The first is that the y-intercept is the turning point If this is the case, the turning point is at (0, c) It is also well known that if the turning point is on the y-axis, that b = 0 So that would mean \displaystyle -\frac{b}{2a} = 0 as well and therefore works as a formula for finding the turning point when the turning point is on the y-axis
- Why is the axis of symmetry of a parabola x=-b 2a? : r learnmath - Reddit
And if you're somehow not convinced by this, take two points on either side of -b 2a, say -b 2a-k and -b 2a+k, plug them both in to ax 2 +bx+c, and verify that you get the same expression In this case, they both work out to ak 2-b 2 4a+c So the height k units to the left of x=-b 2a is the same as the height k units to the right of x=-b 2a
- Help!! What is -b 2a and what is (b 2)^2 What are they used . . . - Reddit
x + b 2a = + – sqrt(b 2 – 4ac) 2a Solve for x by subtracting b 2a from both sides x = –b 2a + – sqrt(b 2 – 4ac) 2a That is the formula for solving the quadratic The x = -b 2a value is the midpoint between the two solutions It is also the x-coordinate of the vertex of the parabola graph
- When deriving the quadratic formula through completing the . . . - Reddit
to figure out what that thing is, suppose it factors as (x+🍉) 2 expanding this and comparing coefficients, we get x 2 + 2🍉x + 🍉2 = x2 + b a x + something, which means 2🍉 = b a so 🍉 = b (2a) therefore the "something" we have to add to complete the square is 🍉2 = (b (2a))2
- Pre-Calc: Why is -b 2a the x-coordinate of a parabolas vertex . . . - Reddit
( x + b (2a) )² = (b (2a))² - c a x+b (2a) = ±√((b (2a))²-c a) x = -b (2a) ± √((b (2a))²-c a) When you solve for the roots (where the parabola crosses the horizontal x-axis, so y=0), you get an equation of the form x = u ± v The number u is perfectly in the center between u-v and u+v, and in the equation above, u = -b (2a)
- Does anyone have an explanation for this? : r learnmath - Reddit
So the graph of a(x + b (2a)) 2 + c - b 2 2a is just the graph of a(x + b (2a)) 2 moved up by c - b 2 2a units, and hence both of these graphs are going to have the same x-value of the vertex Similarly, for a constant K, the graph of y = K f(x) is just the same as the graph of y = f(x) except it's been "stretched" vertically by a factor of K
- Why is -b 2a always going to be the x coordinate of the vertex . . . - Reddit
= a(x + b 2a) 2 + (c - b 2 4a) Notice how the left hand part is a square, and the right hand part doesn't involve x, that is, it's a constant A square must always be positive over real numbers, so it reaches a minimum maximum (depending on the sign + -, of a) when it is zero It's not hard to see that x + b 2a = 0 when x = -b 2a
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