The vertex of a parabola whose equation is in the form y=ax^2 is always (0,0).
Practice makes perfect
We want to draw the graph of the given function, which has the form y=ax^2, where a is either a positive or a negative number.
y=- x^2
To do so, we will follow four steps.
Find and plot two points on one side of the axis of symmetry.
Plot the corresponding points on the other side of the axis of symmetry.
Sketch the curve.
Step 1
The vertex of anyparabola with an equation following the form y=ax^2 is always (0,0). Since the axis of symmetry is the vertical line through the vertex, its equation is x=0.
Step 2
Now we need to find and plot any two points on one side of the axis of symmetry. For simplicity, we will plot the points whose x-coordinates are 1 and 2. Let's use a table to find the y-coordinates of these points.
x
- x^2
y=- x^2
1
- 1^2
- 1
2
- 2^2
- 4
We found that the points ( 1, - 1) and ( 2, - 4) are on the curve. Let's plot them!
Step 3
We will continue by plotting the corresponding points on the other side of the axis of symmetry. This means that we will reflect the two points we already have across the line x=0.
Note that the y-coordinates do not change, but the x-coordinates have opposite signs.
Step 4
Finally, we connect the five points with a smooth curve. We do not need a straight edge for this!
