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

Question

Question content area bottom
Part 1
Drag each function given above into the area below the appropriate​ graph, depending on which function is represented by which graph.
1.
-10
-8
-6
-4
-2
2
4
6
8
10
-4
4
8
12
16
20
24
x
y

A coordinate system has a horizontal x axis labeled from negative 10 to 10 in increments of 2 and a vertical y axis labeled from negative 6 to 24 in increments of 4. A parabola that opens upward and has its vertex at (5, 4) is graphed on the coordinate system.
2.
-10
-8
-6
-4
-2
2
4
6
8
10
-4
4
8
12
16
20
24
x
y

A coordinate system has a horizontal x axis labeled from negative 10 to 10 in increments of 2 and a vertical y axis labeled from negative 6 to 24 in increments of 4. A parabola that opens upward and has its vertex at (negative 5, 4) is graphed on the coordinate system.
3.
-10
-8
-6
-4
-2
2
4
6
8
10
-4
4
8
12
16
20
24
x
y

A coordinate system has a horizontal x axis labeled from negative 10 to 10 in increments of 2 and a vertical y axis labeled from negative 6 to 24 in increments of 4. A parabola that opens upward and has its vertex at (5, negative 4) is graphed on the coordinate system.
4.
-10
-8
-6
-4
-2
2
4
6
8
10
-4
4
8
12
16
20
24
x
y

A coordinate system has a horizontal x axis labeled from negative 10 to 10 in increments of 2 and a vertical y axis labeled from negative 6 to 24 in increments of 4. A parabola that opens upward and has its vertex at (negative 5, negative 4) is graphed on the coordinate system.

Answer 1

To match the quadratic functions to the given graphs based on their vertex locations, here’s how you can approach it:

1. Identify the Vertex: The vertex of the parabola in a quadratic function of the form \( y = a(x-h)^2 + k \) is given by the point \( (h, k) \).

2. Match Each Graph:

   • Look for the vertex coordinates of each parabola in the graphs.
   • For each piece of information provided about the vertices:
     • Graph 1: Vertex at (5, 4) — This parabola opens upwards and is centered to the right side of the x-axis.
     • Graph 2: Vertex at (-5, 4) — This parabola opens upwards and is centered to the left of the x-axis.
     • Graph 3: Vertex at (5, -4) — This parabola opens upwards and is positioned downwards on the y-axis.
     • Graph 4: Vertex at (-5, -4) — This parabola opens upwards and is also positioned downward but more to the left on the x-axis.

Using these details, you can drag the equations corresponding to their vertices to the appropriate graphs:

• Graph 1: Corresponds to the function with vertex (5, 4).
• Graph 2: Corresponds to the function with vertex (-5, 4).
• Graph 3: Corresponds to the function with vertex (5, -4).
• Graph 4: Corresponds to the function with vertex (-5, -4).

If you have specific equations provided, you can match them based on the vertex coordinates described above. If the equations include additional coefficients different from 1 (i.e., parabolas that might be narrower or wider, or shifted vertically), consider those factors when matching as well.

In conclusion, align the graphs with their respective equations using their vertical and horizontal vertex positions as your primary reference points.