Finding Intercepts from Graphs – College Algebra Lesson 1.1

Q1. List the intercepts for the given graph (Graph 1).

Background

Topic: Intercepts of Functions

This question tests your ability to identify x-intercepts and y-intercepts from a graph. Intercepts are points where the graph crosses the axes.

Key Terms and Formulas:

• x-intercept: The point(s) where the graph crosses the x-axis. At these points, $y = 0$.

• y-intercept: The point where the graph crosses the y-axis. At this point, $x = 0$.

Step-by-Step Guidance

1. Look for all points where the graph crosses the x-axis. These are your x-intercepts. Write down the x-coordinates of these points (where $y = 0$).

2. Find the point where the graph crosses the y-axis. This is your y-intercept. Write down the y-coordinate of this point (where $x = 0$).

3. List the coordinates of all intercepts you found in the previous steps.

4. Double-check each intercept by confirming that the other coordinate is zero at those points.

Try solving on your own before revealing the answer!

Final Answer:

x-intercepts: $(-4, 0), (1, 0), (6, 0)$ y-intercept: $(0, 0.66)$

These are the points where the graph crosses the axes. The x-intercepts have $y = 0$, and the y-intercept has $x = 0$.

Q2. List the intercepts for the given graph (Graph 2).

Background

Topic: Intercepts of Quadratic Functions

This question asks you to find the intercepts of a parabola (a quadratic function) from its graph.

Key Terms and Formulas:

• x-intercept: Where the graph crosses the x-axis ($y = 0$).

• y-intercept: Where the graph crosses the y-axis ($x = 0$).

Step-by-Step Guidance

1. Identify the point(s) where the parabola crosses the x-axis. These are your x-intercepts.

2. Find the point where the parabola crosses the y-axis. This is your y-intercept.

3. Write down the coordinates for each intercept.

Try solving on your own before revealing the answer!

Final Answer:

x-intercept: $(0, 0)$ y-intercept: $(0, 0)$

Both intercepts are at the origin for this graph.

Q3. List the intercepts for the given graph (Graph 3).

Background

Topic: Intercepts of Functions (Quadratic/Polynomial)

This question asks you to find the x- and y-intercepts from a downward-opening parabola.

Key Terms and Formulas:

• x-intercept: Where the graph crosses the x-axis ($y = 0$).

• y-intercept: Where the graph crosses the y-axis ($x = 0$).

Step-by-Step Guidance

1. Look for the point(s) where the graph crosses the x-axis. These are your x-intercepts.

2. Find the point where the graph crosses the y-axis. This is your y-intercept.

3. Write down the coordinates for each intercept you found.

Try solving on your own before revealing the answer!

Final Answer:

x-intercept: $(6, 0)$ y-intercept: $(0, -6)$

These are the points where the graph crosses the axes.