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
agasfer [191]
3 years ago
14

Find the equation of a parabola with a vertical axis and its vertex at the origin and passing through the point (-2, 3)

Mathematics
1 answer:
vredina [299]3 years ago
8 0

a vertical axis, I assume it means a vertical axis of symmetry, thus it'd be a vertical parabola, like the one in the picture below.

\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} y=a(x- h)^2+ k\qquad \qquad \leftarrow vertical\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=0\\ k=0 \end{cases}\implies y=a(x-0)^2+0 \\\\\\ \textit{we also know that } \begin{cases} x=-2\\ y=3 \end{cases}\implies 3=a(-2-0)^2+0\implies 3=4a \\\\\\ \cfrac{3}{4}=a~\hspace{10em}y=\cfrac{3}{4}(x-0)^2+0\implies \boxed{y=\cfrac{3}{4}x^2}

You might be interested in
What is the equation of the line in standard form?
belka [17]

Answer:

y = 6x + 4 \\ slop = 6 \\ y - y0 = slop(x - x0) \\ y - ( - 8) = 6 \times (x - 1) \\ y + 8 = 6x - 6 \\ y = 6x - 6 - 8 = 6x - 14

6 0
2 years ago
Ms. Roberts makes bouquets of flowers. Every bouquet of flowers she makes includes 8 flowers. The table below shows the number o
alukav5142 [94]
She made 28 bouquets of flowers!
7 0
3 years ago
What is the solution to the system of equations? <br><br>6x+2y=6<br><br>7x+3y=5
Stells [14]
The answer is (2,-3)
4 0
3 years ago
Read 2 more answers
PLEASE HELP!! It's due tomorrow.
Delicious77 [7]

Answer:

Step-by-step explanation:

A. Directrix: y = 4-6 = -2

:::::

B. Axis of symmetry: x = 6

Axis of symmetry intersects directrix at (6,-2)

:::::

C . Vertex is halfway between focus and directrix, at (6,1)

:::::

D. The focus lies above the directrix, so the parabola opens upwards.

:::::

E. Focal length p = 1/(4×0.5)

:::::

F. p = 0.5

::::

G. y = 0.5(x-6)² + 1

7 0
2 years ago
Du/dr=(1+sqrt(r))/(1+sqrt(u))_
Maslowich
Solution is supposed to be as follows
<span>u+<span>2 / 3</span><span> u<span>^3/2</span></span>
=r+<span>2 / 3</span><span> r^<span>3/2</span></span> + <span>c</span></span>
4 0
3 years ago
Other questions:
  • For the function y=-3+4 cos(5pi/6(x+4)) what is the minimum value
    11·2 answers
  • Can somebody help me with this
    6·1 answer
  • Solve the following equation. Then place the correct number in the box provided.
    8·2 answers
  • Boston, New York, and Philadelphia are often referred to as the ________ of liberty.
    14·2 answers
  • A company has $14,000 in liabilities and $15,000 in equity. Calculate the company's debt to equity ratio as a percentage.
    13·1 answer
  • Explain how to find 45% of a number
    12·1 answer
  • Suppose there is a 1.7°F drop in temperature for every thousand feet that an
    8·1 answer
  • I need help I am confused
    9·2 answers
  • Anyoneeeeeee knows we thissds
    11·2 answers
  • Plz help! Identify the function represented by the graph or table is linear or nonlinear
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!