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Deffense [45]
3 years ago
11

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

la?
A.y = (x - 4)^2 - 47
B.y = (x - 9)^2 - 47
C.y = (x - 6)^2 - 45
D.y = (x - 8)^2 - 47
Mathematics
2 answers:
stealth61 [152]3 years ago
8 0
X² - 16x + 17 = 0
x² - 16x + 8² - 8² + 17 = 0
(x - 8)² - 64 + 17 = 0
(x - 8)² - 47 = 0 

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

julsineya [31]3 years ago
8 0

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

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