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ICE Princess25 [194]
3 years ago
6

Find the zeros of the function y=x^2-4x-16 by completing the square. Express your answer in simple redical form. Graph the parab

ola using a standar window to see the irrational zeroes.

Mathematics
1 answer:
densk [106]3 years ago
8 0

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

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