24.11.2022

Quadratic function with (-2,4) as the vertex and passes through (-4,-4)

. 1

Step-by-step answer

09.07.2023, solved by verified expert
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Quadratic function with (-2,4) as the vertex, №18009960, 24.11.2022 00:34

Step-by-step explanation:

Vertex form of quadratic function:  Quadratic function with (-2,4) as the vertex, №18009960, 24.11.2022 00:34

where Quadratic function with (-2,4) as the vertex, №18009960, 24.11.2022 00:34 is the vertex

Given:

vertex = (-2, 4)

Quadratic function with (-2,4) as the vertex, №18009960, 24.11.2022 00:34

Given:

point on curve = (-4, -4)

Quadratic function with (-2,4) as the vertex, №18009960, 24.11.2022 00:34

Therefore,

Quadratic function with (-2,4) as the vertex, №18009960, 24.11.2022 00:34

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Mathematics
Step-by-step answer
P Answered by Specialist

f(x)=-2x^2-8x-4

Step-by-step explanation:

Vertex form of quadratic function:  f(x)=a(x-h)^2+k

where (h,k) is the vertex

Given:

vertex = (-2, 4)

\implies f(x)=a(x+2)^2+4

Given:

point on curve = (-4, -4)

\implies f(-4)=-4\\\\\implies a(-4+2)^2+4=-4\\\\\implies a(-2)^2=-4-4\\\\\implies 4a=-8\\\\\implies a = -2

Therefore,

f(x)=-2(x+2)^2+4\\\\\implies f(x)=-2(x^2+4x+4)+4\\\\\implies f(x)=-2x^2-8x-8+4\\\\\implies f(x)=-2x^2-8x-4

Mathematics
Step-by-step answer
P Answered by PhD

f(x) = -2 (x + 2)² - 4  

Step-by-step explanation:

f(x) = a (x - h)² + k     (h , k) is vertex    h = -2     k = -4

pass point (-1 , -6)     f(x) = -6 and x = -1

-6 = a (-1 - (-2))² + (-4)

-6 = a - 4

a = -2

quadratic function: f(x) = -2 (x + 2)² - 4

Mathematics
Step-by-step answer
P Answered by PhD

f(x) = -2 (x + 2)² - 4  

Step-by-step explanation:

f(x) = a (x - h)² + k     (h , k) is vertex    h = -2     k = -4

pass point (-1 , -6)     f(x) = -6 and x = -1

-6 = a (-1 - (-2))² + (-4)

-6 = a - 4

a = -2

quadratic function: f(x) = -2 (x + 2)² - 4

Mathematics
Step-by-step answer
P Answered by Specialist
Vertex form: y=a(x-h)^2+k , with (h,k) as the vertex.

For this, we will be using vertex form. Firstly, plug the vertex into the vertex form equation:

y=a(x-(-3))^2+1\\y=a(x+3)^2+1

Next, we need to solve for a. Plug in (-2,4) into the x and y coordinates to solve for a as such:

4=a(-2+3)^2+1\\4=a(1)^2+1\\4=a+1\\3=a

Putting our equation together, it's y=3(x+3)^2+1

*Additional section*

Standard form: y=ax^2+bx+c

Converting to standard form as such:

y=3(x+3)^2+1\\y=3(x^2+6x+9)+1\\y=3x^2+18x+27+1\\y=3x^2+18x+28

Mathematics
Step-by-step answer
P Answered by PhD

The value of y should be 10 because if you graph these two points you can see that the value of y is 10

Mathematics
Step-by-step answer
P Answered by PhD

The value of y should be 10 because if you graph these two points you can see that the value of y is 10

Mathematics
Step-by-step answer
P Answered by Master
Vertex form: y=a(x-h)^2+k , with (h,k) as the vertex.

For this, we will be using vertex form. Firstly, plug the vertex into the vertex form equation:

y=a(x-(-3))^2+1\\y=a(x+3)^2+1

Next, we need to solve for a. Plug in (-2,4) into the x and y coordinates to solve for a as such:

4=a(-2+3)^2+1\\4=a(1)^2+1\\4=a+1\\3=a

Putting our equation together, it's y=3(x+3)^2+1

*Additional section*

Standard form: y=ax^2+bx+c

Converting to standard form as such:

y=3(x+3)^2+1\\y=3(x^2+6x+9)+1\\y=3x^2+18x+27+1\\y=3x^2+18x+28

Mathematics
Step-by-step answer
P Answered by PhD

y = \frac{1}{2}(x + 6)² + 4

the equation of a quadratic in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here (h, k ) = (- 6, 4 ), hence

y = a(x + 6 )² + 4

To find a substitute (- 2, 12) into the equation

12 = 16a + 4 ( subtract 4 from both sides )

8 = 16a ( divide both sides by 16 )

a = \frac{8}{16} = \frac{1}{2}

y = \frac{1}{2}(x + 6 )² + 4 ← in vertex form

Mathematics
Step-by-step answer
P Answered by PhD

y = \frac{1}{2}(x + 6)² + 4

the equation of a quadratic in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here (h, k ) = (- 6, 4 ), hence

y = a(x + 6 )² + 4

To find a substitute (- 2, 12) into the equation

12 = 16a + 4 ( subtract 4 from both sides )

8 = 16a ( divide both sides by 16 )

a = \frac{8}{16} = \frac{1}{2}

y = \frac{1}{2}(x + 6 )² + 4 ← in vertex form

Mathematics
Step-by-step answer
P Answered by PhD

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

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