What is the vertex form of #y=(x+4)(2x-1)(x-1)#?
Something like:
#f(x) = 2(x+5/6)x^3 - 91/6(x+5/6)+418/27#
The given polynomial is a cubic, not a quadratic. So we cannot reduce it to 'vertex form'.
What is interesting to do is to find a similar concept for cubics.
For quadratics we complete the square, thereby finding the centre of symmetry of the parabola.
For cubics we can make a linear substitution "completing the cube" to find the centre of the cubic curve.
So:
graph{(y-(x+4)(2x-1)(x-1))(40(x+5/6)^2+(y-418/27)^2-0.2) = 0 [-6.13, 3.87, -5, 40]}
So in general we can use this method to get a cubic function into the form:
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The vertex form of ( y = (x + 4)(2x - 1)(x - 1) ) can be found by expanding and simplifying the expression, and then completing the square. After simplification, the vertex form is:
[ y = 2(x + 1/4)^2 - 9/8 ]
This expression represents the same function in a form that explicitly shows the vertex as (-1/4, -9/8).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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