Sketching a Parabola if the xIntercepts Exist
What do you Need to Sketch a
Parabola?
Can you sketch a parabola if you only know where its yintercept is? For example, if the y-intercept of a
parabola is (0,-15) can you sketch the graph? Why or
why not?
NO!
You can NOT
determine
whether it opens
up or down.
What do you Need to Sketch a
Parabola?
Can you sketch a parabola if you only know where its xintercept are? For example, if the x-intercepts of a
parabola are (-3,0) and (5,0) can you sketch the graph?
Why or why not?
NO!
You can NOT
determine
whether it opens
up or down.
What do you Need to Sketch a
Parabola?
Can you sketch a parabola if you only know where its x-intercept and yintercept are? For example, if the x-intercepts of a parabola are
(-3,0) and (5,0) and the y-intercept is (0,-15), can you sketch the
graph? Why or why not?
IMPORTANT:
The vertex
must lie on the
line of
symmetry.
YES!
A third point
helps determine
whether it opens
up or down.
Sketching a Quadratics
Sketch: y = 2x2 + 5x – 12
Find the y-intercept
Pay attention to Symmetry
8
Factor to find the x-intercepts
y  2 x  5x  12
2
0  2 x  5x  12
0   x  4  2 x  3
x  4  0 2x  3  0
2x  3
x  4
x  32
2
Draw the Parabola
-6
6
-16