Question

Ariel completes the square for the equation x2 - 16x + 17 = 0. Which of the following equations reveals the vertex of the parabola?

A.y = (x - 4)^2 - 47
B.y = (x - 9)^2 - 47
C.y = (x - 6)^2 - 45
D.y = (x - 8)^2 - 47

Answer 1

x² - 16x + 17 = 0
x² - 16x + 8² - 8² + 17 = 0
(x - 8)² - 64 + 17 = 0
(x - 8)² - 47 = 0

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Answer: y = (x - 8)² - 47 (Answer D)
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Answer 2

Option D is correct

`y = (x-8)^-47`

Explanation:

A quadratic equation is in the form of
`y=ax^2+bx+c`,

then the vertex form of the quadratic equation using the completing square method is given as:

`y =(x-h)^2+k` where, vertex = (h, k)

As per the statement:

Ariel completes the square for the equation:
`x^2-16x+17 = 0`

Using completing square method:

1.

subtract 17 from both sides we have;

`x^2-16x = -17`

2.

Complete the square on the left side of the equation and balance this by adding
`8^2 = 64` to the right side of the equation.

then;

`x^2-16x+8^2= -17+64`

Using identity rules on left side:

`(a-b)^2 = a^2-2ab+b^2`

then;

`(x-8)^2 = 47`

we can write this as:

`y = (x-8)^-47`

Therefore, the equations reveals the vertex of the parabola is,
`y = (x-8)^-47`