Test yourself: the graph of the parabola

Given the standard equation of the parabola [math]y=ax^2+bx+c[/math]. [br]ObServe how the graph is changing its shape if you move the black, red and green points on the sliders. which correspond with the coefficiente a,b and c of the parabola equation.[br]

a) if changes the coefficient a of x[sup]2[/sup] we observe that .......................(one or more answers are likely to be correct)

the parabola get upsidedown the parabola opens upwards if a<0 the parabola opens upwards if a>0 the parabola opens or closes its path

b) if changes the coefficient b of x we observe that .......................

if b>0 the Vertex belongs to the second or third dial if b<0 the Vertex belongs to the first or fourth dial if b<0 the Vertex belongs to the second or third dial if b>0 the Vertex belongs to the first or fourth dial

c) if changes the coefficient c we observe that .......................

the parabola traslates vertically the parabola traslates horizontally

d) if a=0 we observe that .......................[br]

the parabola becomes a straight line the parabola becomes a cubic function

e) if b=0 we observe that .......................[br]

the parabola has two opposite intersections with the x-axes if c is negative the parabola has two opposite intersections with the x-axes if c is positive

if c=0 we observe that...............

the parabola doesn't pass through the origin the parabola passes through the origin

– Prof.ssa Maiolino Daniela

Information: Test yourself: the graph of the parabola