Question

What is the vertex of the graph of the function below?

Answer 1

Answer:          

The correct answer is B. (4, -4)

Step-by-step explanation:

The equation of the graph is given to be : y = x² - 8x + 12

Now, comparing the given equation with standard form : ax² + bx + c

⇒ a = 1 , b = -8 and c = 12

$\text{Also, The x-value of the vertex is given by }\frac{-b}{2a}$

$\text{So, The x-value of the vertex = }\frac{8}{2}=4$

So, The x-value of the vertex = 4

Now, Putting this value of x in the given equation to find the y-value of the vertex :

⇒ y = 4² - 4 × 8 + 12

⇒ y = 16 - 32 + 12

⇒ y = -4

Hence, The vertex of the given equation is (4, -4)

Therefore, The correct answer is B. (4, -4)

Answer 2

Since y = x2 - 8x + 12 is a quadratic equation, it is the same of y=ax²+bx+c
the main formula of the vertex is x= -b/2a, and y=f(-b/2a)

for our case x= -(-8) / 2=4, and f(4)= -4

the answer is B. (4, -4)