Question

Find the zeros of the function y=x^2-4x-16 by completing the square. Express your answer in simple redical form. Graph the parabola using a standar window to see the irrational zeroes.

Answer 1

Answer:

The zeros of the function are

$x=2+2\sqrt{5}$

$x=2-2\sqrt{5}$

The graph in the attached figure

Step-by-step explanation:

we have

$y=x^{2}-4x-16$

This is a vertical parabola open upward (the leading coefficient is positive)

The vertex is a minimum

Remember that

The zeros of the function are the values of x when the value of y is equal to zero

For y=0

$x^{2}-4x-16=0$

Move the constant term to the right side

$x^{2}-4x=16$

Complete the square

$x^{2}-4x+2^2=16+2^2$

$x^{2}-4x+4=20$

Rewrite as perfect squares

$(x-2)^{2}=20$ ---> the vertex is the point (2,-20)

take square root both sides

$x-2=\pm\sqrt{20}$

$x=2\pm\sqrt{20}$

Simplify

$x=2\pm2\sqrt{5}$

The zeros of the function are

$x=2+2\sqrt{5}$

$x=2-2\sqrt{5}$

using a graphing tool

The graph in the attached figure