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
Mila [183]
3 years ago
15

Suppose a parabola has an axis of symmetry at x=-5, a maximum height of 9, and passes through the point (-7,1). Write the equati

on of the parabola in vertex form.

Mathematics
1 answer:
Nutka1998 [239]3 years ago
7 0

the parabola has maximum at 9, meaning is a vertical parabola and it opens downwards.

it has a symmetry at x = -5, namely its vertex's x-coordinate is -5.

check the picture below.

so then, we can pretty much tell its vertex is at (-5 , 9), and we also know it passes through (-7, 1)


\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} y=a(x- h)^2+ k\qquad \leftarrow \textit{using this one}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-5\\ k=9 \end{cases}\implies y=a[x-(-5)]^2+9\implies y=a(x+5)^2+9


\bf \textit{we also know that } \begin{cases} x=-7\\ y=1 \end{cases}\implies 1=a(-7+5)^2+9 \\\\\\ -8=a(-2)^2\implies -8=4a\implies \cfrac{-8}{4}=a\implies -2=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-2(x+5)^2+9~\hfill

You might be interested in
WHAT DOES THIS MEAN I DONT UNDERSTAND
Art [367]

Answer:

the goal is to try and get x alone. For the 1st problem, x=3.

Step-by-step explanation:

3x + 1 = 10      Subtract 1 both sides to cancel out the 1 on the left side. 10-1 = 9

3x = 9             To get x alone here, Divide 3 on both sides. 9/3 = 3

x = 3                Now x is alone, which means x = 3.

This is right because if you plug x with 3, the sum = 10.

(3*3) + 1 =10

9 + 1 = 10

So, that's how you know 3 is the right answer.

3 0
2 years ago
Answer to this please
xenn [34]

Answer:

(150 \times 75 - 75 \times 75 \times 3.14 \times 0.5) \times 0.5 = (11250 - 8831.25) \times 0.5 = 1209.375

5 0
3 years ago
Which of the following is a reasonable estimate for the weight capacity of an elevator that can carry up to 15 people?
Bas_tet [7]

A is the most common

6 0
3 years ago
Read 2 more answers
Determine if the set of ordered pairs is a relation or a function.
MariettaO [177]

Answer:

Function

Step-by-step explanation:

Since there is once variable of y for ever6y value of x in (-1,2), (-2,1), (-3,0), (-4,-1), this relation is a function.

8 0
3 years ago
Two divers are swimming at different depths below sea level. One diver is at -25.5 ft. The other diver is at -40.75 ft. How far
-Dominant- [34]

Answer:

66.25 ft

Step-by-step explanation:

25.5 + 40.75

66.25

They are 66.25 feet away from each other.

Please let me know if I'm wrong!

5 0
3 years ago
Other questions:
  • So…I have been making 0’s on my math homework…cause I don’t understand it.
    10·1 answer
  • What is 3x+2x(x-1)=9x+4
    15·1 answer
  • Find the following from the table:<br> m = _______<br> b = _______<br> Equation: _______
    15·1 answer
  • F(x)=7x-17/x^2+6x+9 <br>solve using fractional decomposition
    13·1 answer
  • What is the value of the expression? (-3)(-4)(-5)
    12·1 answer
  • Math test help!!!!!!
    9·1 answer
  • Doug's teacher told him that the standardized score (z-score) for his mathematics
    6·1 answer
  • Write an equation of the line in slope-intercept form given the graph below.
    10·1 answer
  • Can someone help me? Plss
    14·1 answer
  • Please help me solve this
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!