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

Answer:

Option D is correct

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

Step-by-step 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, $y = (x-8)^-47$