Finding X and Y Intercepts of Polynomial Functions

TLDR; Finding the intercepts of a polynomial function in factored form involves setting y=0 for x-intercepts and x=0 for y-intercepts, then solving for the respective variable. The x-intercepts are found by setting y=0 and solving for x, while the y-intercept is determined by setting x=0 and solving for y. The x-intercepts are the roots of the function and the y-intercept is the point where the graph crosses the y-axis.

⚙️ Understanding the Problem

Given a polynomial function in factored form, the task is to find the x and y intercepts of the function.

To find the x-intercepts, the process involves setting y=0 and solving for x. On the other hand, to find the y-intercept, x is set to 0 and solved for y.

It's important to note that in function notation, 'f of x' is equivalent to 'y'.

🔍 Finding X-Intercepts

To find the x-intercepts, the equation is set to 0 and solved for x. In this case, the function is set to zero and solved for x.

The product of the factors of the function is set equal to 0, which helps in finding the x-intercepts.

The x-values where each factor is equal to 0 represent the x-intercepts of the function, which are the roots of the function.

📈 Expressing X-Intercepts

The x-intercepts are technically represented by vertical lines and are expressed as ordered pairs, such as (2,0), (-1,0), (4,0), and (-3,0).

The x-intercepts can also be listed as individual x-values, namely 2, -1, 4, and -3.

It's important to note that expressing the x-intercepts as ordered pairs provides coordinate points on the graph.

🔄 Determining Y-Intercept

To determine the y-intercept, x is set to 0 and the function is solved for y, or in function notation, 'f of 0' is calculated.

The product of the factors when x=0 yields the y-intercept of the function, which is the point where the graph crosses the y-axis.

In this case, the y-intercept is found to be 24, which can also be expressed as the coordinate point (0,24).

📊 Verification Through Graphing

The accuracy of the x and y-intercepts can be confirmed by graphing the function.

In the graph, the x-intercepts are observed at -3, -1, 2, and 4 on the x-axis, while the y-intercept appears to be at 24.

The graph serves as a visual verification of the correctness of the calculated x and y-intercepts.