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Scrat [10]
3 years ago
5

Help with some algebra please?

Mathematics
1 answer:
kipiarov [429]3 years ago
7 0
Vertex form is   f(x) = a(x - b)^2 + c    where the vertex is (b, c) and a is some constant.

So for the first part we have  f(x) = a(x + 6)^2 - 1

for root -9:-  a( -9+6)^2 - 1 = 0
9a - 1 = 0 , a = 1/9

The other 3 are derived in the same way.
so required equation is f(x) = (1/9)(x + 6)^2 - 1




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The value of x<em> </em>in the polynomial fraction 3/((x-4)•(x-7)) + 6/((x-7)•(x-13)) + 15/((x-13)•(x-28)) - 1/(x-28) = -1/20 is <em>x </em>= 24

<h3>How can the polynomial with fractions be simplified to find<em> </em><em>x</em>?</h3>

The given equation is presented as follows;

\frac{3}{(x - 4) \cdot (x - 7) }  + \frac{6}{(x - 7) \cdot (x - 13)   }  + +\frac{15}{(x - 13) \cdot (x - 28) } - \frac{1}{(x - 28)  } =  -  \frac{1}{20}

Factoring the common denominator, we have;

\frac{3\cdot(x - 13) \cdot(x - 28) + 6 \cdot(x - 4) \cdot(x - 28)  + 15 \cdot(x - 4) \cdot(x - 7)  - (x - 4) \cdot (x - 7)\cdot(x - 13)}{(x - 4) \cdot (x - 7)\cdot(x - 13) \cdot(x - 28)}   + =  -  \frac{1}{20}

Simplifying the numerator of the right hand side using a graphing calculator, we get;

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-(x³ - 48•x + 651•x - 2548)

Given that the terms of the numerator have several factors in common, we get;

-(x³ - 48•x + 651•x - 2548) = -(x-7)•(x-28)•(x-13)

Which gives;

\frac{-(x - 7) \cdot(x - 28)\cdot (x - 13)}{(x - 4) \cdot (x - 7)\cdot(x - 13) \cdot(x - 28)}   + =  -  \frac{1}{20}

Which gives;

\frac{-1}{(x - 4)}   + =  -  \frac{1}{20}

x - 4 = 20

Therefore;

  • x = 20 + 4 = 24

Learn more about polynomials with fractions here:

brainly.com/question/12262414

#SPJ1

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