Question

Use the parabola tool to graph the quadratic function f(x)=−(x−2)(x+4).

Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

Answer 1

Find the Vertex:

To find the vertex of the parabola, you can use the formula for the x-coordinate of the vertex of a quadratic function in the form of f(x) = a(x - h)^2 + k:

In your case, a = -1, h = 2, and k = 0.

The x-coordinate of the vertex is h = 2.

Plot the Vertex:

Plot the vertex at (2, 0).

Find Another Point:

To find another point on the parabola, you can choose an x-value other than 2 and calculate the corresponding y-value. For simplicity, you can choose x = 0:

f(0) = -(0 - 2)(0 + 4) = -(2)(4) = -8

So, when x = 0, y = -8.

Plot the Second Point:

Plot the second point at (0, -8).

Now you have the vertex (2, 0) and another point (0, -8) on the graph of the quadratic function f(x) = -(x - 2)(x + 4). You can connect these points to sketch the parabola.