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
STALIN [3.7K]
2 years ago
13

F(x) = -x^2+ 6x -10 write each function in vertex form and give the vertex

Mathematics
1 answer:
Pani-rosa [81]2 years ago
6 0

Answer:

Vertex form: f(x) = – (x – 3)² – 1  

vertex: (3, -1)

Step-by-step explanation:

Given the quadratic function, f(x) = -x²+ 6x -10:

where a = -1, b = 6, and c = -10

The vertex of a parabola is the point at which the parabola intersects the axis of symmetry. The <u>axis of symmtery</u> occurs at x = h. Therefore, the x-coordinate of the vertex is the same as <em>h. </em>

To find the vertex, (<em>h</em>, <em>k</em>), you need to solve for <em>h </em>by using the formula:  h = \frac{-b}{2a}

Plug in the values into the formula:

h = \frac{-b}{2a}

h = \frac{-6}{2(-1)} = 3

Therefore, h = 3.

Next, to find the <em>k</em><em>, </em>plug in the value of<em> </em><em>h</em> into the original equation:

f(x) = -x²+ 6x -10

f(x) = -(3)²+ 6(3) -10

f(x) = -1

Therefore, the value of h = -1.

The vertex = (3, -1).

Now that you have the value for the vertex, you can plug these values into the vertex form:

f(x) = a(x - h)² + k

<em>a</em> =  determines whether the graph opens up or down, and makes the parent function wider or narrower.

  • If <em>a</em> is positive, the graph opens <u>up</u>.
  • If<em> </em><em>a</em><em> </em>is negative, the graph opens <u>down</u>.

<em>h</em><em> </em>= determines how far left or right the parent function is translated.

<em>k</em> = determines how far up or down the parent function is translated.

Plug in the vertex, (3, -1) into the vertex form:

f(x) = – (x – 3)² – 1  

This parabola is downward-facing, with its vertex, (3, -1) as its maximum point on the graph.

You might be interested in
What is the answer if you factor completely
Sergeeva-Olga [200]

Answer:

Your correct and final answer is (9+x^6) (3+x^3) (3-x^3)

Hope this helps!!!


3 0
3 years ago
Ax + z = aw - y<br> Solve for a
olga2289 [7]
Ax=aw-z-y
divide by x
a=awx-z-y
a=awx-zy
8 0
3 years ago
Its math help me out
Anvisha [2.4K]

Answer:

each one is double the one before it so in year 5...

3912*2=7824

Hope This Helps!!!

7 0
2 years ago
Read 2 more answers
Describe how to determine which side of the boundary line should be shaded
iogann1982 [59]
Hello Bri,

If you are talking about a boundary line on a coordinate plane, the best way to determine which side to shade is to start by selecting a coordinate point (x, y) that is not on the line.

Then, substitute those values into your inequality. Simplify the inequality. If the resulting statement is true, then shade the side with your point. If the resulting statement is false, then shade the other side.

Testing a point like this shows the side of the inequality that is the solution and needs to be shaded.

Good luck!
8 0
3 years ago
If 6 people shared 5 blocks of clay evenly, how much would everyone get?
Lena [83]
Divide the number of blocks by number of people In this case 5/6 = 0.83 blocks or each person will get 0.83 or 5/6 of a block
5 0
3 years ago
Other questions:
  • 1. Your bank account has -$15 in it. You deposit $5 per day. (a) How much money is in your account after 5 days? Show your work.
    5·2 answers
  • What is 400 percent as a mixed number?
    15·1 answer
  • Use substitution to solve the system of equations. y=x +1.74 4x-2y =4
    15·1 answer
  • Find the value of x . round the nearest hundredth . <br><br>A.12.37<br>B.7.51<br>C.10.63<br>D.9.79
    13·1 answer
  • Consider U = {x|x is a positive integer greater than 1}.
    9·2 answers
  • Help please! this is algebra. It says it needs to be in a fractional exponent form ONLY!​
    10·1 answer
  • What is the first error Holden made in his proof?
    7·2 answers
  • Help with finals please <br> !! I will make you brainliest! Please
    11·1 answer
  • four glasses of milk and 2 snack bars have a total of 68 carbohydrates​ (carbs), and 2 glasses of milk and 3 snack bars have a t
    7·1 answer
  • Write an expression equivalent to -4(x+3)-12x+5 that only has two terms
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!