Question

the graph of a quadratic function is given. match the equation with its graph.

drag each of the following functions into the area with the matching graph.

\\(h(x) = (x - 2)^2 + 4\\)
\\(g(x) = (x + 2)^2 + 4\\)
\\(j(x) = (x - 2)^2 - 4\\)
\\(f(x) = (x + 2)^2 - 4\\)

Explanation:

Understand vertex form

Using the Quadratic Equations knowledge point

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

The vertex of the parabola is located at the point \((h, k)\).

Analyze Graph 1

The vertex of the parabola in Graph 1 is located at \((-2, -4)\).
Matching with the vertex form:

$$ f(x) = (x - (-2))^2 + (-4) = (x + 2)^2 - 4 $$

Analyze Graph 2

The vertex of the parabola in Graph 2 is located at \((-2, 4)\).
Matching with the vertex form:

$$ g(x) = (x - (-2))^2 + 4 = (x + 2)^2 + 4 $$

Analyze Graph 3

The vertex of the parabola in Graph 3 is located at \((2, 4)\).
Matching with the vertex form:

$$ h(x) = (x - 2)^2 + 4 $$

Analyze Graph 4

The vertex of the parabola in Graph 4 is located at \((2, -4)\).
Matching with the vertex form:

$$ j(x) = (x - 2)^2 - 4 $$

Answer:

No.	Answer
2	\(g(x) = (x + 2)^2 + 4\)
3	\(h(x) = (x - 2)^2 + 4\)
4	\(j(x) = (x - 2)^2 - 4\)