All categories

3 years ago

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

Mathematics

2 answers:

olasank [31]3 years ago

5 0

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)

Free_Kalibri [48]3 years ago

3 0

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)

You might be interested in

Convert the following into standard form y = -x + 1/3

Doss [256]

y = -x + 1/3
+ x + x
--------------------------
x + y = 1/3

5 0

3 years ago

The graph of f(x) = x2 + x - 6 is shown below.

guapka [62]

Answer:

the solutions of a function are the points where for some value of x the function becomes zero

thus the solns for this graph would be

that's option 1.

3 0

3 years ago

Find the four rational numbers and irrational numbers between 2/5 and 5/6

Savatey [412]

The four?

Of course there are an infinite number of rationals between any two different real numbers, as well as an even bigger infinite number of irrationals.

The average will be between the numbers:

$\frac 1 2 (\frac 2 5 + \frac 5 6) = \dfrac{37}{60}$

That's a lot of work to get a number in between. We can just see

$\frac 1 2$
is between the two numbers.

The mediant, or freshman addition, will always be in between:

$\dfrac{2 + 5}{5 + 6} = \dfrac{7}{11}$

2/5=.4 and 5/6 is about .83, so

$.6 = \frac{6}{10}$

is in between as is .7, .41, .530940394 and as many rationals as we care to generate.

To get irrationals we could just add a teeny irrational to the ones we just generated, like $\frac{6}{10} + \frac{\pi}{100}$

We could just change that denominator a bit and get as many as we like.

But let's get some square roots. The geometric mean will be between

$\sqrt{ \dfrac 2 5 \cdot \dfrac 5 6 } = \dfrac{1}{\sqrt{3}}
$

That's the tangent from one of trig's biggest cliches, but I digress. It's in between.

While we're on trig cliches,

$\dfrac{1}{\sqrt{2}}$

is in between as well.

Keeping with the trig theme, also in between are

$\dfrac{\pi} 6$

and

$\dfrac{\pi}{4}$

the angles associated with the some of the above trig function values.

We could obviously go on as long as we cared to.

7 0

3 years ago

A gym charges a monthly fee and an additional cost for each class. Consider the graph that represents the relationship between t

bija089 [108]

For this problem you need to understand that a linear graph is a straight line (Remember Rise/Run).
A continous function is a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output, so we can already cross off that as an answer.
The Y-Intercept is the cost (in dollars), so this would be to monthly fee.
Now, onto the rate of change. The rate of change is represented by the slope of a line. So the more classes you take the more it will increase. Therefore the cost for one class is the rate of change.
Lastly, the cost for one class is $10. It's not, since $10 is the intial fee to belong to a gym, so this is false.

Recap:
True
-The relationship is linear
-The y-intercept represents the monthly fee.
-The rate of change represents the cost for one class.
False
-The relationship represents a continuous function.
-The cost for one class is $10.
I hope I've helped you, have a great day!

7 0

3 years ago

The equation for a circle is x2+10x+y2+12y+52=0 .

aev [14]

I believe the answer is (x+5)^2+(y+6)^2=9

8 0

3 years ago

Read 2 more answers