Step-by-step explanation:
Vertex form of quadratic function:
where is the vertex
Given:
Therefore,
f(x) = -2 (x + 2)² - 4
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
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
It will provide an instant answer!