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Scilla [17]
3 years ago
9

Using the completing-the-square method, rewrite f(x) = x2 − 8x + 3 in vertex form.

Mathematics
1 answer:
lys-0071 [83]3 years ago
8 0
          f(x) = x² - 8x + 3
             y = x² - 8x + 3
           - 3                - 3
        y - 3 = x² - 8x + 16
y - 3 + 16 = x² - 8x + 16
     y + 13 = x² - 8x + 16
     y + 13 = (x - 4)²
         - 13      - 13
             y = (x - 4)² - 13
          f(x) = (x - 4)² - 13
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What’s the answer of a multiplying polynomials (3x-1) to the second power and (x+6) to the second power
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9x^4+102x^3+253x^2-204x+36 is the result of multiplying (3x-1) to the second power and (x+6) to the second power

<h3><u>Solution:</u></h3>

Given that we have to find the result of multiplying polynomials (3x-1) to the second power and (x+6) to the second power

"Second power" means the term is raised to power of 2

Therefore,

We have to multiply (3x-1)^2 \text{ and }(x+6)^2

\rightarrow (3x-1)^2 \times (x+6)^2

We can use the algebraic identity to expand the above expression

(a+b)^2 = a^2+2ab+b^2\\\\(a-b)^2=a^2-2ab+b^2

Applying these in above expression, we get

\rightarrow ((3x)^2-2(3x)(1)+1^2) \times (x^2+2(x)(6)+6^2)\\\\\rightarrow (9x^2-6x+1) \times (x^2+12x+36)

Multiply each term in first bracket with each term in second bracket

\rightarrow 9x^2(x^2)+(9x^2)(12x)+(9x^2)(36)-6x(x^2)-6x(12x)-6x(36) + x^2+12x+36

Simplify the above expression

\rightarrow 9x^4+108x^3+324x^2-6x^3-72x^2-216x+x^2+12x+36

Combine the like terms

\rightarrow 9x^4+102x^3+253x^2-204x+36

Thus the above expression is the result of multiplying (3x-1) to the second power and (x+6) to the second power

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