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Ilya [14]
3 years ago
9

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) = x^{2} +x-7
Mathematics
1 answer:
mrs_skeptik [129]3 years ago
3 0

Answer:

Vertex form: f(x) =(x +\frac{1}{2})^2 -\frac{29}{4}

The vertex is (-\frac{1}{2},-\frac{29}{4})

Step-by-step explanation:

For a general quadratic function the form is:

ax ^ 2 + bx + c

For the function

f(x) = x ^ 2+ x -7

The values of the coefficients for the function are the following: a = 1, b =1, c = -7

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

\frac{b}{2}= \frac{1}{2}

(\frac{b}{2})^2=(\frac{1}{2})^2=\frac{1}{4}

Add and subtract \frac{1}{4}

f(x) = (x ^ 2 +x +\frac{1}{4}) -\frac{1}{4}- 7

Write the expression of the form

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

f(x) =(x +\frac{1}{2})^2 -\frac{29}{4}

The vertex is (h, k)

The vertex is: (-\frac{1}{2},-\frac{29}{4})

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