Respuesta :
The given function is
[tex]f(x)=x^2+5x-2[/tex]The vertex has two coordinates, h, and k. To find h we use the following formula.
[tex]h=-\frac{b}{2a}[/tex]Where a = 1 and b = 5.
[tex]h=-\frac{5}{2(1)}=-\frac{5}{2}[/tex]Then, we evaluate the function when x = -5/2 to find k.
[tex]\begin{gathered} k=f(-\frac{5}{2})=(-\frac{5}{2})^2+5(-\frac{5}{2})-2 \\ k=\frac{25}{4}-\frac{25}{2}-2 \end{gathered}[/tex]Let's find the least common factor between the denominators.
4 2 | 2
2 1 | 2
1
The least common factor would be 2*2 = 4, let's use it.
[tex]\begin{gathered} k=\frac{25-2\cdot25-4\cdot2}{4} \\ k=\frac{25-50-8}{4} \\ k=-\frac{33}{4} \end{gathered}[/tex]Once we know the value of h and k, we can deduct the vertex.
Therefore, the vertex is (-5/2, -33/4).
The standard form of a quadratic function is
[tex]f(x)=a(x-h)^2+k[/tex]In this case, a = 1, h = -5/2, and k = -33/4.
