Question

Graph f(x) = x^2 + 4x and label its key features.

Key Features:
A) Classification: Parabola
B) x-intercept: (-4, 0)
C) y-intercept: (0, 0)
D) Increasing / decreasing: Increasing
E) Positive / negative: Positive
Explanation: To work this out, first find the x-intercept and y-intercept, and then observe the shape and direction of the graph.

Answer 1

The graph of the function f(x) = x² + 4x is added as an attachment

Sketching the graph of the function

From the question, we have the following parameters that can be used in our computation:

f(x) = x² + 4x

Set x to 0 to calculate the y-intercept

f(0) = 0² + 4(0)

f(0) = 0

So, we have the y-intercept: (0, 0)

Set y to 0 to calculate the x-intercept

x² + 4x = 0

x(x + 4) = 0

x = 0 and x = -4

So, we have the x-intercept: (0, 0) and (-4, 0)

The above function is a quadratic function that has the following features

Parabola

• x-intercept: (-4, 0)
• y-intercept: (0, 0)
• Increasing / decreasing: Increasing
• Positive / negative: Positive

The graph of the function is added as an attachment