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Explain the Vertex Formula ?
The vertex formula is a convenient way of finding the vertex of the graph for any quadratic function. The graph of the quadratic equation f(x) = ax2 + bx + c has its vertex at:
(-b/2a, f(-b/2a))
In other words the x coordinate of the vertex is always x = -b/2a, which is also the equation for the axis of symmetry.
SymmetryNote: this formula is derived from the standard form by completing the square.Here's an example that you can look at:
Question: Use the vertex formula to find the vertex of the graph of the following function:f(x) = -x 2 + 6x - 5 Solutions: Find the x-coordinate of the vertex first, using the vertex formula. x = -b /2aX = -6 / 2(-1)X = -6/-2X =3This tells us that the vertex is the point (3, ?). We now need to find the y-coordinate, or functional value, forx = 3. f(3) = -(3) 2 + 6(3) - 5= -9 + 18 -5= 4So, the vertex point of f(x) = -x2 +6x - 5 is the point (3,4)
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FORMULAS DERIVATION
Solve by factorization X 2 +(a/a+b + a+b/a)x+1 = 0 X 2 +(a/a+b + a+b/a)x+1 => X 2 +(a/a+b x a+b/ax + a/a+b .a+b/a) => X[x+a/a+b] +a+b/a[a+a*a+b]= 0 => X= -a
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how do you add 1,ooo and 100?
Important formulas d (a b )/ dx = 0 This is a constant d ( x n ) / dx = nx n -1 Power Rule d (a x ) / dx = a x l
y=6sin3x,find dy/dx
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