Finding the x- and y- Intercepts of an Equation (3.5.2)

Question 1

• An x-intercept is a point where a curve crosses the x-axis.

Answer 1

• An x-intercept is a point where a curve crosses the x-axis.

Question 2

• A y-intercept is a point where a curve crosses the y-axis.

Answer 2

• A y-intercept is a point where a curve crosses the y-axis.

Question 3

• A line will have one x-intercept and one y-intercept (with the exception of horizontal or vertical lines).

Answer 3

• A line will have one x-intercept and one y-intercept (with the exception of horizontal or vertical lines).

Question 4

• A curve may have more than one of either intercept. A curve may have none of either or both intercepts.

Answer 4

• A curve may have more than one of either intercept. A curve may have none of either or both intercepts.

Question 5

Significant points on any curve are the points where the curve crosses each of the two axes. The curve crosses the y-axis at any point where x = 0. The curve crosses the x-axis at any point where y = 0. To find the x-intercept, let y = 0, and solve for x. In this case, x = 6 where y = 0.
So the x-intercept is at the point (6, 0). To find the y-intercept, let x = 0, and solve the equation for y.
In this example, y = 12/5 when x = 0. So the y-intercept is at the point. Now that you have two points on the line, graphing the line becomes fairly simple. To find the y-intercept, let x = 0 and solve. In this case, y = 3 is a quick find. To find the x-intercept, let y = 0 and solve. Factoring is required to find there are two x-intercepts,
x = 3 and x = 1. Now draw a quick sketch of the curve to see what we have. It’s a matter of placing the points and connecting the dots to show us that we have a parabola for this equation. This equation follows the exact same procedures as the two examples above. Find an x-intercept: when y = 0, x = 12. Find y-intercepts: when x = 0, y = 6 and y = –2. Graphing this one again reveals a parabola, but one opening to the left. Using these intercepts gives a quick and easy way to sketch the graph of an equation. Using them lets us visually understand what the equation is saying.

Answer 5

Significant points on any curve are the points where the curve crosses each of the two axes. The curve crosses the y-axis at any point where x = 0. The curve crosses the x-axis at any point where y = 0. To find the x-intercept, let y = 0, and solve for x. In this case, x = 6 where y = 0.
So the x-intercept is at the point (6, 0). To find the y-intercept, let x = 0, and solve the equation for y.
In this example, y = 12/5 when x = 0. So the y-intercept is at the point. Now that you have two points on the line, graphing the line becomes fairly simple. To find the y-intercept, let x = 0 and solve. In this case, y = 3 is a quick find. To find the x-intercept, let y = 0 and solve. Factoring is required to find there are two x-intercepts,
x = 3 and x = 1. Now draw a quick sketch of the curve to see what we have. It’s a matter of placing the points and connecting the dots to show us that we have a parabola for this equation. This equation follows the exact same procedures as the two examples above. Find an x-intercept: when y = 0, x = 12. Find y-intercepts: when x = 0, y = 6 and y = –2. Graphing this one again reveals a parabola, but one opening to the left. Using these intercepts gives a quick and easy way to sketch the graph of an equation. Using them lets us visually understand what the equation is saying.