Answer:
Vertex form: [tex]f(x) =(x +\frac{7}{2})^2 -\frac{53}{4}[/tex]
The vertex is [tex](-\frac{7}{2},-\frac{53}{4})[/tex]
Step-by-step explanation:
For a general quadratic function the form is:
[tex]ax ^ 2 + bx + c[/tex]
For the function
[tex]f(x) = x ^ 2+ 7x -1[/tex]
The values of the coefficients for the function are the following: [tex]a = 1[/tex], [tex]b =7[/tex], [tex]c = -1[/tex]
Take the value of b and divide it by 2. Then, the result obtained squares it.
[tex]\frac{b}{2}= \frac{7}{2}[/tex]
[tex](\frac{b}{2})^2=(\frac{7}{2})^2=\frac{49}{4}[/tex]
Add and subtract [tex]\frac{49}{4}[/tex]
[tex]f(x) = (x ^ 2 +7x +\frac{49}{4}) -\frac{49}{4}- 1[/tex]
Write the expression of the form
[tex]f(x) = (x+\frac{b}{2})^2 +k[/tex]
[tex]f(x) =(x +\frac{7}{2})^2 -\frac{53}{4}[/tex]
The vertex is [tex](-\frac{7}{2},-\frac{53}{4})[/tex]
