Respuesta :
Option A
The vertex is (h, k) = (5, -25)
Solution:
Given function is:
[tex]f(x) = x^2-10x[/tex]
The vertex form is given as:
[tex]y = a(x-h)^2+k[/tex]
where (h, k) is the vertex
Rewrite the equation in vertex form
[tex]f(x) = x^2-10x[/tex]
Complete the square for [tex]x^2-10x[/tex]
Use the form [tex]ax^2+bx+c[/tex] to find the values of a, b, c
a = 1 , b = -10, c = 0
Consider the vertex form of a parabola
[tex]a(x+d)^2+e[/tex]
Substitute the values of a and b into the following formula to find "d" :
[tex]d = \frac{b}{2a}\\\\d = \frac{-10}{2 \times 1}\\\\d = -5[/tex]
Find the value of "e" using the formula,
[tex]e = c - \frac{b^2}{4a}\\\\e = 0 - \frac{(-10)^2}{4 \times 1}\\\\e = -25[/tex]
Substitute the value of a, d, e into vertex form
[tex]a(x+d)^2+e\\\\1(x-5)^2-25\\\\(x-5)^2-25[/tex]
Set y equal to above equation
[tex]y = (x-5)^2-25[/tex]
Compare the above equation with vertex form
[tex]y = a(x-h)^2+k[/tex]
[tex]y = (x-5)^2-25[/tex]
We find, h = 5 and k = -25
Thus the vertex is (h, k) = (5, -25)
