graphing quadratic equation

1. Graphing quadratic equation
Presented by : Claire Gui

2. quadratic equation
 ax2
+by=c
 a,b,c are constants
a+b=c
ax2
+by=c
a+b=c

3. symbolic-graphic combination
 ax2
+by=c
 vertical parabola
ax2
+by=c
a+b=c

4. What will the parabola be like?
 a=b
 x2
+y=2
opens down
vertex (0,2)
ax2
+by=c
a+b=c

5. What will the parabola be like?
 c=0
 x2
-y=0
opens up
vertex (0,0)
ax2
+by=c
a+b=c

6. What will the parabola be like?
 a,b,c are all positive or negative numbers
 x2
+y=2 2x2
+y=3 3x2
+y=4 4x2
+y=5
y-coordinate of vertex
is getting bigger
the parabola is
getting wider
opens down
ax2
+by=c
a+b=c

7. What will be the parabola like?
 a ＞ 0 b ＜ 0 c ＜ 0 or a ＜ 0 b ＞ 0 c ＞ 0
 x2
-2y=-1 x2
-3y=-2 x2
-4y=-3
y-coordinate of the
vertex is getting bigger
the parabola is getting
wider
opens up.
ax2
+by=c
a+b=c

8. What will be the parabola like?
 a and b are fractions, c=1
y-coordinate of the
vertex is getting larger
the parabola is getting
narrower
opens down
ax2
+by=c
a+b=c

9. What will be the parabola like?
 If either a or b becomes zero, the equation will be
showed as a straight line.
ax2
+by=c
a+b=c

10. What will the line be like?
 a=0
 by=c=b → y=1
straight line
ax2
+by=c
a+b=c

11. What will the line be like?
 b=0
 ax2
=c=a → x2
=1
two straight lines
x=1 and x=-1
ax2
+by=c
a+b=c