Test yourself: the graph of the parabola

Given the standard equation of the parabola

. 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.

a) if changes the coefficient a of x² we observe that .......................(one or more answers are likely to be correct)

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A
the parabola opens or closes its path
B
the parabola get upsidedown
C
the parabola opens upwards if a<0
D
the parabola opens upwards if a>0

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

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A
if b>0 the Vertex belongs to the first or fourth dial
B
if b>0 the Vertex belongs to the second or third dial
C
if b<0 the Vertex belongs to the first or fourth dial
D
if b<0 the Vertex belongs to the second or third dial

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

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A
the parabola traslates horizontally
B
the parabola traslates vertically

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d) if a=0 we observe that .......................

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

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e) if b=0 we observe that .......................

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

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

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

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Test yourself: the graph of the parabola

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