Today, students will be able to:
- Determine x-intercepts by factoring, then solving a quadratic equation.
- Notice patterns when graphing parabolas (quadratic equations)
- Graph a parabola based on a vertex
I recommend you have a piece of paper to jot down notes or scratch work (I needed it!)
Match the standard form of each quadratic with its factored form.
| Draggable item | arrow_right_alt | Corresponding Item |
|---|---|---|
| arrow_right_alt | ||
| arrow_right_alt | ||
| arrow_right_alt |
Match each equation with its solutions.
| Draggable item | arrow_right_alt | Corresponding Item |
|---|---|---|
0=(x+2)(x-5) | arrow_right_alt | x=-3 and x=5 |
0=(x+1)(x-5) | arrow_right_alt | x=-2 and x=5 |
0=(x+3)(x-5) | arrow_right_alt | x=-1 and x=5 |
Match each set of solutions (also known as x-intercepts) with it's graph. If you're unsure, just focus on where the parabola crosses the x-axis.
| Draggable item | arrow_right_alt | Corresponding Item |
|---|---|---|
(-2,0) and (5,0) | arrow_right_alt |
|
(-1,0) and (5,0) | arrow_right_alt |
|
(-3,0) and (5,0) | arrow_right_alt |
|
I'd prefer to have you complete an (x,y) table, but because I can't, we'll do this a different way.
Given the equation
What is the value of y when x=-3
*remember that a negative times a negative is a positive!
Given the equation
What is the value of y when x=-2
*Remember that a negative times a negative is a positive- your calculator might lie to you!
Given the equation
What is the value of y when x=-1
*Remember that a negative times a negative is a positive- your calculator might lie to you!
Given the equation
What is the value of y when x=0
Given the equation
What is the value of y when x=1
Given the equation
What is the value of y when x=2
Given the equation
What is the value of y when x=3
The vertex is the lowest (or highest if the parabola has a negative a-value, but we're focusing on positive for this class) point on a parabola. That means it has the lowest y-value. What are the coordinates for the vertex of
Here is the table of the (x,y) values you found in the previous problems.
Type your coordinates as (x,y)
Move from the vertex of (0,0) in the table in both directions and see if you can figure out the pattern in the y-values. What would the y-values in the blank boxes be?
Graph the equation
To do this, you will type y=x^2 and the parabola should appear on the graph.
Use the board and graph (the best you can) to see if you can show the pattern you figured out from number #12.
What happens if you add 3 to the equation? Match each x-value with its y-value for the new equation.
| Draggable item | arrow_right_alt | Corresponding Item |
|---|---|---|
-2 and 2 | arrow_right_alt | 12 |
0 | arrow_right_alt | 7 |
-3 and 3 | arrow_right_alt | 4 |
-1 and 1 | arrow_right_alt | 3 |
Graph the equation
To do this, you will type y=x^2+3 and the parabola should appear on the graph.
Keeping in mind the "1, 3, 5" pattern, what is the y-value for the missing boxes?
Some people used the "1-3-5" pattern to fill in the previous table, and others may have done the math in their head or on the calculator. With an equation like the one below, using the pattern can be a little easier. If (-2,1) is the vertex (highlighted), use the "1-3-5" pattern to figure out the value for x=-3 and x=-1.
I don't suggest actually plugging in the x-values, just focus on the pattern. I also suggest you just write this table and complete it- the next few problems will go much faster.
What is the y-value for x=-4 and x=0
What is the value of y when x=-5 and x=1
Below is the graph of
If we go out one unit from the labeled points, how many should we go up to find the next two points?
The equation
has a vertex of (4,-9). If we graph according to the "1-3-5" pattern, what will the first two points be? I've included a graph with the vertex on it in case you're better visually. (list them left to right for easier scoring)
If I were doing this, I would graph the whole thing and write the coordinates you find on paper so you can easily enter them in the next few problems.
The equation
has a vertex of (4,-9). If we graph according to the "1-3-5" pattern, what will the next two points be? The graph now has the vertex and the first two points.
What are the next two points in the pattern?
The equation
has a vertex of (-4,-1) which has been placed on the graph in the "Show your work" box. Graph the next six points. Then watch the video to check your work.
The equation
has a vertex of (-4,-1) which has been placed on the graph in the "Show your work" box. Graph the next six points. Then watch the video to check your work.
