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2 years ago

Find the quadratic function represented by the following graph.

Mathematics

1 answer:

nikdorinn [45]2 years ago

6 0

Answer:

f(x) = (-3/4)x^2 + 3

Step-by-step explanation:

First, look at the vertex to see if it intersects the y-axis. It does, which is good, because it makes your job a lot easier by making your equation to fill out y = ax + b. Your b is the y value of your vertex, which in this case is 3. Then, your a is the amount you're multiplying plain old x^2 by to get your values (before adding 3). Because the graph is pointing down, you know right away that it's going to be negative. Also, going to the left or right by 2 (the points you are given) from the vertex gives you a result of going down 3. Normally this would mean you move up by 4 (again, from the vertex), so what do you need to multiply 4 by to get -3? -3/4, so that's your a. This makes your equation (y OR) f(x) = (-3/4)x^2 + 3

I hope I didn't make any mistakes reading your graph! I had a bit of difficulty with it unfortunately.

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Pleasee help mee<br><br>12sin(x)-5cos(x)=6,5

abruzzese [7]

We turn -5,12 into polar coordinates. It's a Pythagorean Triple so

r = 13 Ф=arctan(-12/5) + 180° ( in the second quadrant )

so -5 = 13 cos Ф, 12 = 13 sin Ф

12 sin x - 5 cos x = 6.5

13 sinФ sin x + 13 cos Ф cos x = 6.5

13 cos(x - Ф) = 6.5

cos(x - Ф) = 1/2

cos(x - Ф) = cos 60°

x - Ф = ± 60° + 360° k integer k

x = Ф ± 60° + 360° k

x = 180° + arctan(-12/5) ± 60° + 360° k

That's the exact answer;

x ≈ 180° - 67.38° ± 60° + 360° k

x ≈ 122.62° ± 60° + 360° k

x ≈ { 62.62°, 182.62°} + 360° k, integer k

3 0

3 years ago

i need help. Semir, Sarah, and SungSo decided to raise money for a local homeless shelter by working in a local deli. The deli a

IgorLugansk [536]

According to the question,
Let,
"n" represent the number of miles semir walked.
"y" represent the number of miles sarah walked.
Now, according to the question,

y = 2n - 5 ........................this is your equation
Also,
the question states, each of them collect $18 in pledges for every miles walked.

Given,
Sarah collected $450
Now,

Using unitary method,

Sarah collects $18 for 1 mile
Sarah collects $1 for (1 / $18) mile
Sarah collects $450 for (1 / 18) * 450 mile
= 25 miles
So, Sarah walks 25 miles.
Now,
Taking equation,
y = 2n - 5
Since, y is the no. of miles sarah walked, we can write 25 in place of "y" So,
(25) = 2n - 5
25 + 5 = 2n
30 = 2n
30 / 2 = n
15 = n

Since, "n" is the no. of miles that semir walked, Semir walked 15 miles.

7 0

3 years ago

Solve the systems of equations y=2x and y=-x - 6

slava [35]

Answer:

y = -4

x = -2

Step-by-step explanation:

Hi there...

y = 2x

y = -x - 6

Since why is equal to 2x, we can plug it in for y in the second equation. Here's what I mean...

2x = -x - 6

add x on both sides...

3x = -6

divide by 3 on both sides...

x = -2

Now, plug in x for y. Here's what I mean...

y = 2x

y = 2 (-2)

y = -4

Hope this helps :)

7 0

3 years ago

Please help!

crimeas [40]

Answer:

The zeros are:

$x =4, x=2, x = 5$

The function has three distinct real zeros.

Hence, option (B) is true.

Step-by-step explanation:

Given the expression

$h\left(x\right)=\left(x-4\right)^2\left(x^2-7x+\:10\right)$

Let us determine the zeros of the function by putting h(x) = 0 and solving the expression

$0=\left(x-4\right)^2\left(x^2-7x+10\right)$

switch sides

$\left(x-4\right)^2\left(x^2-7x+10\right)=0$

$x^2-7x+\:10=\left(x-2\right)\left(x-5\right)$

$\left(x-4\right)^2\left(x-2\right)\left(x-5\right)=0$

Using the zero factor principle

$\mathrm{If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)$

$x-4=0\quad \mathrm{or}\quad \:x-2=0\quad \mathrm{or}\quad \:x-5=0$

$x =4, x=2, x = 5$

Thus, the zeros are:

$x =4, x=2, x = 5$

It is clear that there are three zeros and all the zeros are distinct real numbers.

Therefore,

The function has three distinct real zeros.

Hence, option (B) is true.

4 0

3 years ago

Factorise x2 + 13x + 42

kirill [66]

Answer:

you can use the formula "<em>Cross method" </em> in which the last number of the equation is the sum of 2 number multiplication that also sums the 2nd num of the equation.

so it becomes

(x +6)(x +7)

WHY?

Bcs when u multiply 6 x 7 = 42 ( the last number of the equation)

when u sum 6 + 7 = 13 ( the 2nd number of the equation)

Hope this helps :)

8 0

3 years ago

Find the quadratic function represented by the following graph.​

Find the quadratic function represented by the following graph.