Effect: A negative coefficient makes the parabola open downward.
Practice makes perfect
To sketch a graph, we need to know some points through which it passes. Therefore, we will start by making a table of values for the first function.
x
x^2
y
-2
( -2)^2
4
-1
( -1)^2
1
0
0^2
0
1
1^2
1
2
2^2
4
Let's mark the points in a coordinate plane and connect the dots with a smooth curve.
Next, we repeat this process for the second function.
x
-2 x^2
y
-2
- 2 ( -2)^2
-8
-1
- 2( -1)^2
-2
0
- 2 ( 0^2)
0
1
- 2 ( 1^2)
-2
2
- 2( 2^2)
-8
Then we continue with the third function.
x
- 0.5 x^2
y
-2
- 0.5 ( -2)^2
-2
-1
- 0.5( -1)^2
-0.5
0
- 0.5 ( 0^2)
0
1
- 0.5 ( 1^2)
-0.5
2
- 0.5( 2^2)
-2
Let's plot these points in the same diagram and draw their parabolas.
Notice that the function with a positive coefficient to x^2 opens upward, whereas the functions that have negative coefficient open downward. Thus, a negative coefficient makes the parabola open downward.
