whitakers87
30.01.2021 •
Mathematics
4x^2 -5x+2x^2-8x^3+9-3x
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Ответ:
Simplified:
− 8 x ^3 + 6 x ^2 − 8 x + 9
It is the same thing in standard form.
Step-by-step explanation:
I hope this helps! Have a nice day!
Ответ:
3rd degree normal form is f(x)=ax^3+bx^2+cx+d
We know that a 3rd degree function with a positive leading coefficient (a) will go from bottom left to top right.
With a negative leading coefficient, it goes from top left to bottom right.
We know that a is negative.
multiplicities
When a point goes through, it has odd multiplicity, in this case, 1
When it is is tangent, it has an even multiplicity or in this case, 2
We see the intercepts are at x=-3 and at x=2, the x=-3 passes through 1 time but at x=2, it is tangent or bounces off the x axis.
with roots r₁ and r₂, the equation is (x-r₁)(x-r₂)
the roots are x=-3 and x=2, but x=2 appears 2 times so
(x-(-3))(x-2)^2=(x+3)(x-2)(x-2)
remember that it has negative leading coefficient
f(x)=-(x+3)(x-2)(x-2)
f(x)=(3-x)(x-2)(x-2)
or expanded
f(x)=-x³+x²+8x-12