About this video
A short algebra video on finding the y-intercept of a quadratic function written in standard form. The instructor explains that the y-intercept is the y value where x equals zero, and shows that substituting x = 0 eliminates the x-squared and x terms, leaving the constant term 9 as the answer K.
You'll be able to
- define the y-intercept of a graph.
- find the y-intercept of a quadratic by substituting x equals zero.
- explain why the x-squared and x terms vanish at x equals zero.
Key words
- Y-intercept
- The point where a graph crosses the Y axis, which is the y value when x equals zero.
- Standard form
- Writing a quadratic as ax squared plus bx plus c, with its constant term c.
- Constant term
- The term with no variable, which is the value that remains when x equals zero.
- X-intercept
- The point where a graph crosses the X axis, which is where y equals zero.
Transcript
- [Instructor] We're told the graph of Y is equal to three X squared minus 12 X plus nine is shown right over here. If the graph crosses the Y axis at the point 0,K, what is the value of K? Pause this video and see if you can work through this. All right. So the graph crosses the Y axis at the point 0.
So the X coordinate is zero. Y coordinate is K. So it's at this point, right over here. We would also call that the Y intercept, which is the Y value when the X coordinate is equal to zero. And to figure that out we just have to look back to the equation. I'll just rewrite it.
Y is equal to, and we see that it's written in standard form, three X squared, minus 12 X plus nine. And so what is Y going to be equal to when X is equal to zero? Well, when X equals zero, that term's just going to be zero. When X is equal to zero this term's going to be equal to zero.
And so Y is going to be equal to nine. And that is choice C and we're done.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.