Question

What is the vertex of the function f (x) = x2 - 10x?(5,-25)(5.-75)(-5,75)(-5,25)​

Answer 1

Option A

The vertex is (h, k) = (5, -25)

Solution:

Given function is:

$f(x) = x^2-10x$

The vertex form is given as:

$y = a(x-h)^2+k$

where (h, k) is the vertex

Rewrite the equation in vertex form

$f(x) = x^2-10x$

Complete the square for  $x^2-10x$

Use the form $ax^2+bx+c$ to find the values of  a, b, c

a = 1 , b = -10, c = 0

Consider the vertex form of a parabola

$a(x+d)^2+e$

Substitute the values of a and b into the following formula to find "d" :

$d = \frac{b}{2a}\\\\d = \frac{-10}{2 \times 1}\\\\d = -5$

Find the value of "e" using the formula,

$e = c - \frac{b^2}{4a}\\\\e = 0 - \frac{(-10)^2}{4 \times 1}\\\\e = -25$

Substitute the value of a, d, e into vertex form

$a(x+d)^2+e\\\\1(x-5)^2-25\\\\(x-5)^2-25$

Set y equal to above equation

$y = (x-5)^2-25$

Compare the above equation with vertex form

$y = a(x-h)^2+k$

$y = (x-5)^2-25$

We find, h = 5 and k = -25

Thus the vertex is (h, k) = (5, -25)