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