Graphing quadratic equationPresented by : Claire Gui

quadratic equation

ax2+by=c a,b,c are constants a+b=c

ax2+by=ca+b=c

symbolic-graphic combination ax2+by=c

vertical parabola

ax2+by=ca+b=c

What will the parabola be like? a=b x2+y=2

opens downvertex (0,2)

ax2+by=ca+b=c

What will the parabola be like? c=0 x2-y=0

opens upvertex (0,0)

ax2+by=ca+b=c

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 biggerthe parabola is getting wideropens down

ax2+by=ca+b=c

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=ca+b=c

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 narroweropens down

ax2+by=ca+b=c

What will be the parabola like? If either a or b becomes zero, the equation will be showed as a straight line.

ax2+by=ca+b=c

What will the line be like? a=0 by=c=b → y=1

straight line

ax2+by=ca+b=c

What will the line be like? b=0 ax2=c=a → x2 =1

two straight linesx=1 and x=-1

ax2+by=ca+b=c