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

Step-by-step explanation:

Vertex form of quadratic function:  

where is the vertex

Given:

Given:

Therefore,

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

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

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

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

Putting our equation together, it's

*Additional section*

Converting to standard form as such:

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

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

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

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

Putting our equation together, it's

*Additional section*

Converting to standard form as such:

y = (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 = =

y = (x + 6 )² + 4 ← in vertex form

y = (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 = =

y = (x + 6 )² + 4 ← in vertex form

The answer is in the image