Introduction to Parabolas
While the graph of a linear equation is a straight line, the graph of a quadratic equation is a curve called a parabola. Parabolas are more complicated to graph than lines, but they have distinct features and properties that you can use to help with graphing. This lecture series explores what all parabolas have in common and how to use them to model real-life situations. Watch the videos and complete the interactive exercises.
Parabolas intro - Questions
Answers
1. C.
.Let's review each option.
This parabola intersects the 
-axis at two points.
This parabola doesn't intersect the -axis at all! (Yes, this can happen with parabolas.
This parabola touches the -axis with its vertex. Therefore, it has exactly one -intercept.
Note that whenever a parabola has exactly one -intercept, that intercept will be the vertex, and the parabola will be touching the -axis instead of crossing it.
2. We start with a vertex. This vertex is either the minimum or the maximum point of the parabola.
Since the 
-intercept is below the vertex, we know the parabola opens down.
This is the parabola.
3. The vertex of a parabola is the lowest or highest point of the parabola (depending on whether the parabola opens up or down).
The vertex is also the parabola's intersection with its axis of symmetry.
The vertex of our parabola is at 
.
4. The first thing we have to do in order to graph the parabola is find its vertex.
We are given that the parabola's minimum value is 
, so we know the vertex's -coordinate is 
.
We can find the vertex's -coordinate by taking the average of the two -intercepts:
So the vertex is at 
.
In order to graph, we need one more point on the parabola. We can use one of the given -intercepts, like 
.
