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8 months ago

Write an equation for the parabola who’s vertex is at (3,6) and which passes through (4,4)

Mathematics

1 answer:

Gekata [30.6K]8 months ago

4 0

Problem

Solution

For this case we know that the vertex is given by (3,6) and the genera equation for a parabola is given by:

y= a(x-h)^2 +k

Where h = 3, k=6 and replacing we have:

y= a(x-3)^2 +6

And we can find the value of a with the point given x= 4, y=4

4= a(4-3)^2 +6

4= a +6

a= 4-6=-2

And the correct equation would be:

d. y= -2(x-3)^2 +6

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Please help solve for x..

aalyn [17]

Answer:

x = 1 or x = -1

Step-by-step explanation:

Given equation:

$x^{100}-4^x \cdot x^{98}-x^2+4^x=0$

Factor out -1:

$\implies -1(-x^{100}+4^x \cdot x^{98}+x^2-4^x)=0$

Divide both sides by -1:

$\implies -x^{100}+4^x \cdot x^{98}+x^2-4^x=0$

Rearrange the terms:

$\implies 4^x \cdot x^{98}-4^x-x^{100}+x^2=0$

$\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c \quad \textsf{to }x^{100}:$

$\implies 4^x \cdot x^{98}-4^x-x^{98}x^2+x^2=0$

Factor the first two terms and the last two terms separately:

$\implies 4^x(x^{98}-1)-x^2(x^{98}-1)=0$

Factor out the common term $(x^{98}-1)$ :

$\implies (4^x-x^2)(x^{98}-1)=0$

Zero Product Property: If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Using the Zero Product Property, set each factor equal to zero and solve for x (if possible):

$\begin{aligned}x^{98}-1 & = 0 & \quad \textsf{or} \quad \quad4^x-x^2 & = 0 \\x^{98} & =1 & 4^x & = x^2 \\x & = 1, -1 & \textsf{no}& \textsf{ solutions for } x \in \mathbb{R}\end{aligned}$

Therefore, the solutions to the given equation are: x = 1 or x = -1

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3 0

1 year ago

If the problem says x=5 ,did it give you a input or output?

Thepotemich [5.8K]

It gave you the input because it is telling you what x is

8 0

2 years ago

Read 2 more answers

PLEASE HELP I HAVE 5 MIN TO TURN THIS IN!!!!

Lady_Fox [76]

Answer:

False

Step-by-step explanation:

Perimeter of garden A is

P = 2(w + l) = 2( 2x - 3 + 5(2x - 3)) = 24x - 36

Perimeter of garden B is

5x + 5 + 4x + 2 + 8x - 8 = 17x - 1

Sum of perimeters:

24x - 36 + 17x - 1 = 41x - 37

The statement 2 is FALSE as number we got is different from the one in the statement

6 0

2 years ago

Read 2 more answers

Pls help I need ASAP pls

eimsori [14]

Answer:

-1

Step-by-step explanation:

The line goes down 1 grid square for each grid square to the right. Each grid square represents 1 unit in both the x- and y-directions. That means the slope is ...

m = rise/run = -1/1 = -1

The slope of the line is -1.

6 0

2 years ago

Which points are on the graph of ƒ(x) = 2(0.5)^x

Slav-nsk [51]

x y=2*(0.5)^x

-10 2048 
-9 1024
 -8 512 
-7 256 
-6 128
 -5 64
 -4 32 
-3 16
-2 8 
-1 4 
0 2 
1 1 
2 0.5 
3 0.25
 4 0.125 
5 0.0625 
6 0.03125 
7 0.015625
 8 0.0078125 
9 0.00390625
 10 0.00195313

As x goes to negative infinity the function grows to infinity.

As x grows to infinity the function decreases an approximate to zero.

5 0

3 years ago