1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ololo11 [35]
3 years ago
15

The function f(x)=x^2 -6x+3 is transformed such that g(x)=f(x-2). Find the vertex of g(x).

Mathematics
1 answer:
Lisa [10]3 years ago
5 0

Answer:

g(x) = (x-2)^2 -6(x-2) +3

g(x) = x^2 -4x +4 -6x +12 +3

g(x) = x^2 -10 x +19

g(x) = x^2 -10 x + 25 +19 -25

g(x) = (x-5)^2 -6

y= (x-h)^2 -kk

Where h,k represent the vertex and we got:

(h,k)= (5,6)

(5,6)

Step-by-step explanation:

We have this original function given :

f(x) = x^2 -6x +3

And we want to find the vertex for this new function g(x) = f(x-2) and we have:

g(x) = (x-2)^2 -6(x-2) +3

And solving the square we got:

g(x) = x^2 -4x +4 -6x +12 +3

And adding similar terms we got:

g(x) = x^2 -10 x +19

Now we can complete the square like this:

g(x) = x^2 -10 x + 25 +19 -25

g(x) = (x-5)^2 -6

The general equation is given by:

y= (x-h)^2 -kk

Where h,k represent the vertex and we got:

(h,k)= (5,6)

(5,6)

You might be interested in
Find the exact values of cos 3 pi/4 radians sin 3 pi/4 radians.
Liula [17]
If you consult the unit circle, you will see that:

cos(\frac{3\pi}{4}) = -\frac{\sqrt{2}}{2}\\\\sin(\frac{3\pi}{4}) = \frac{\sqrt{2}}{2}

3pi/4 in degrees is 3pi/4 * 180/pi = 3/4 * 180 = 135 degrees. And please refer to the attachment to how you can obtain the values above.

Now, lets multiply it together.

-\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2} =\\\\-\frac{2}{4} =\\\\ \boxed{\bf{-\frac{1}{2}}}

So, <span>cos(3pi/4)sin(3pi/4) = -1/2</span>

7 0
3 years ago
The new e-reader measures 8 inches long, 5 inches wide, and 2 inches deep. which is the correct unit of measurement to use when
Diano4ka-milaya [45]
Inches cubed. Or inches^3
4 0
3 years ago
Read 2 more answers
Brainliest to the first correct answer!
Goryan [66]

Answer:

D.

Step-by-step explanation:

You know that 0.25 went to 2.00. That means that it's a 1.75 jump. In order to jump the other two prices up and keep the ratio the same, you must also jump them 1.75.

0.05 + 1.75 = 1.80

0.10 + 1.75 = 1.85

To double check the ration we can look back on the original. 0.05 to 0.10 is a scale of 0.05. 0.10 to 0.25 is a scale of 0.15

Then we look at our new one. 1.80 to 1.85 is a scale of 0.05. 1.85 to 2.00 is a scale of 0.15.

The ratios stayed the same, so this is the correct answer.

I hope this helped :)

7 0
3 years ago
Read 2 more answers
Need some serious help ASAP (will give brainliest)
abruzzese [7]
I could be wrong (and I apologize if I am), but I believe these are the answers to your questions.

1.) Angle 4
2.) Angle 6
3.) Angle 10
4.) 30 degrees
5.) 48 degrees
6.) 55 degrees
7.) 68 degrees
8.) 148 degrees
9.) 102 degrees
10.) 38 degrees

If I turn out to be correct, then I am happy I was able to help you.
3 0
2 years ago
Consider the line 7x+9y=5
alisha [4.7K]

Answer:

The slope of a line parallel to this line will be: -7/9

The slope of the perpendicular line will be:

\frac{-1}{\frac{-7}{9}}=\frac{9}{7}

Step-by-step explanation:

We know the slope-intercept form

y=mx+b

Here,

  • m is the slope
  • b is the y-intercept

Given the equation

7x+9y=5

simplifying to write in the lope-intercept form

y=-\frac{7}{9}x+\frac{5}{9}

Thus, the slope of the line is: -7/9

The slope of a line parallel to the line:

We have already determined that the slope of the line is: -7/9

  • We know that the parallel lines have the same slope.

Thus, the slope of a line parallel to this line will be: -7/9

The slope of a line perpendicular to the line:

We have already determined that the slope of the line is: -7/9

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line.

Thus,  the slope of the perpendicular line will be:

\frac{-1}{\frac{-7}{9}}=\frac{9}{7}

4 0
3 years ago
Other questions:
  • Will 5 1/5 x 2/5 be larger or smaller than 5 1/5
    10·1 answer
  • A survey was done that asked people to indicate whether they run or ride a bike for exercise.
    7·2 answers
  • Find the exponential function that satisfies the given conditions: Initial value = 31, increasing at a rate of 10% per year
    11·1 answer
  • Rewrite in simplest rational exponent form √x • 4√x.
    7·2 answers
  • For every 1/150 square mile Xavier mows, Boa mows 1/120square miles. How many square miles does Xavier mow for every 1 square mi
    5·1 answer
  • (HELPING WITH 6TH GRADE HOMEWORK)
    11·1 answer
  • 2x+29=5x+20 solve for x. x=???????
    10·1 answer
  • Which is greater three hours or 300 minutes
    7·2 answers
  • Duane recorded the temperature outside his window one morning. On the second day,
    14·1 answer
  • A 450-square-foot apartment in New York City costs $540,000. What is the price per square foot?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!