Question

Transform the given quadratic function into vertex form f(x) = quadratic function into vertex form f(x) = quadratic function into vertex form $f(x) = (x-h)^{2} + k$ by completing the square. $a(x-h)^{2} +k$ by completing the square.
$f(x) = x^{2} +7x-1$

Answer 1

Answer:

Vertex form: $f(x) =(x +\frac{7}{2})^2 -\frac{53}{4}$

The vertex is $(-\frac{7}{2},-\frac{53}{4})$

Step-by-step explanation:

For a general quadratic function the form is:

$ax ^ 2 + bx + c$

For the function

$f(x) = x ^ 2+ 7x -1$

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

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

$\frac{b}{2}= \frac{7}{2}$

$(\frac{b}{2})^2=(\frac{7}{2})^2=\frac{49}{4}$

Add and subtract $\frac{49}{4}$

$f(x) = (x ^ 2 +7x +\frac{49}{4}) -\frac{49}{4}- 1$

Write the expression of the form

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

$f(x) =(x +\frac{7}{2})^2 -\frac{53}{4}$

The vertex is $(-\frac{7}{2},-\frac{53}{4})$