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
jekas [21]
2 years ago
5

If h(x) represents a parabola whose turning point is at (0, -3) and the function f is defined by

Mathematics
1 answer:
Elena L [17]2 years ago
8 0

let's put h(x) in vertex form, and then let's see if we can get f(x) from there.

~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{vertex}{\stackrel{h}{0}~~,~~\stackrel{k}{-3}}\qquad h(x)=a(x-0)^2-3 \\\\[-0.35em] ~\dotfill

h(x+2)=a[(x+2)-0]^2-3\implies h(x+2)=\underline{a(x+2)^2-3} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{llll} \underline{h(x+2)}-5\implies [a(x+2)^2-3]~~ - ~~5\implies &\boxed{a(x+2)^2-8=f(x)} \\\\ &a[x-\stackrel{h}{(-2)}]^2\stackrel{k}{-8}=f(x)\\\\ &\stackrel{vertex}{-2~~,~~-8} \end{array}

You might be interested in
What is this this sos 3x-y=3? (x,y)=?
Mazyrski [523]
Rewrite the equation; 

3x-y=3 
3x-3=y 

Linear equation.

I'm unsure of what the second part asks. Can you rewrite the given question?
6 0
3 years ago
Write an equation to match each graph:
morpeh [17]

Write an equation to match each graph.

Solution:

The first graph is V shaped graph centered at origin, (0,0) and the graph is not shifted or translated. So, the equation of first graph is,

y=|x|

The second graph is V shaped graph centered at (1,0) and y=|x| is horizontally shifted right by 1 unit. So, the equation of second graph is,

y=|x-1|

The third  graph is also V shaped but, it is inverted V graph centered at (0,1) . As, the graph is inverted V So, the graph must have y=-|x|. But, as the center is (0,1). So, the graph is shifted up by 1 unit. So, the equation of the third graph is,

y=-|x|+1

The fourth graph is shifted V graph, whose center is (1,-1). So, y=|x| is shifted right by 1 unit and down by 1 unit. So, the equation of fourth graph is,

y=|x-1|-1

The center of fifth graph is (-1,0), So, y=|x| graph is shifted left by 1 unit. So, the equation of fifth graph is

y=|x+1|

5 0
3 years ago
Read 2 more answers
Calculus:Derivatives
otez555 [7]
(x − 8)(y − 4) = 50, so y = 4 + 50 x−8 . Then A(x) = x 4 + 50 x − 8 
x > 8. A 0 (x) = 4 − 400 (x − 8)2 , so A 0 (x) = 0 gives x = 18.
 A 00(x) = 800 (x − 8)3 > 0
so the function is concave up, so x = 18 is the absolute minimum. When x = 18, y = 9. 
8 0
3 years ago
H*es on me left and..
son4ous [18]

Answer:

gl*ck 9 put em out like a light

Step-by-step explanation:

Coupe tinted like a thief in the night

4 0
3 years ago
Which set of ordered pairs could represent a linear function <br><br> (please help!!)
vlabodo [156]
The answer is A- (3,5), (5,1), (7,-2), (9,-6)
4 0
3 years ago
Read 2 more answers
Other questions:
  • Which statement is true about the expression 12-7+3
    11·2 answers
  • I will give BRAINLIEST to whoever is CORRECT
    9·1 answer
  • Simplify the product by using FOIL <br><br> (6x-5)(2x-3)
    11·1 answer
  • Some whole numbers are irrational numbers? True or False?
    10·2 answers
  • The two figures above are similar. The perimeter of quadrilateral ABCD is 50 cm, and the perimeter of quadrilateral EFGH is 75 c
    6·2 answers
  • Solve the formula 12x+2y=10 for y
    11·2 answers
  • Please someone help me
    14·2 answers
  • You and your friend skate at the same rate. You complete 5 laps in 7 minutes. How long does your friend take
    10·2 answers
  • Can someone please help me thank you
    8·1 answer
  • 12y + 8 - 4 + 12y simplified.
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!