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Paul [167]
3 years ago
6

Transform the given quadratic function into vertex form f(x) = quadratic function into vertex form f(x) = quadratic function int

o vertex form f(x) =  (x-h)^{2} + k by completing the square. a(x-h)^{2} +k by completing the square.
f(x) = 3x^{2} -4x-6
Mathematics
1 answer:
vesna_86 [32]3 years ago
3 0

Answer:

f(x) = 3(x -\frac{2}{3})^2 -\frac{22}{3}

The vertex is (\frac{2}{3}, -\frac{22}{3})

Step-by-step explanation:

For a general quadratic function the form is:

ax ^ 2 + bx + c

For the function

f(x) = 3x ^ 2 -4x -6

Take common factor 3.

f(x) = 3(x ^ 2 -\frac{4}{3}x - 2)

The values of the coefficients for the function within the parenthesis are the following: a = 1, b = -\frac{4}{3}, c = -2

Take the value of b and divide it by 2. Then, the result obtained squares it.

\frac{b}{2}= -\frac{2}{3}

(\frac{b}{2})^2=\frac{4}{9}

Add and subtract \frac{4}{9}

f(x) = 3([x ^ 2 -\frac{4}{3}x +\frac{4}{9}]- 2-\frac{4}{9})

Write the expression of the form

f(x) = (x-\frac{b}{2})^2 +k

f(x) = 3(x -\frac{2}{3})^2 -\frac{22}{3}

The vertex is (\frac{2}{3}, -\frac{22}{3})

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