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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)
writing sin 3 a.cos 3 a = sin 3 a.cos 2 a.cosa = sin 3 a.(1-sin 2 a).cosa put sin a as then cos a da = dt integral(t 3 (1-t 2 ).dt = integral of t 3 - t 5 dt = t 4 /4-t 6 /6
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3 multiplied by 5 by 3
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