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1. It is possible for a cubic function to have no turning point.

2. The number of solutions for ax^3 + bx^2 +cx + d = 0 ranges from 1 to 3

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I learnt that a cubic equation can have 3 x-intercepts and also that it is possible for a cubic equation to have no turning point.

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1. It is possible for a cubic function to not have a turning point

2. The number of solutions for a cubic equation ranges from 1 to 3

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One thing i have learnt from this lesson is how to sketch a cubic functions graph.

Another thing i have learnt from this lesson is some cubic graphs do not have turning points.

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I have learnt how the value of a affects the shape of the graph

I have learnt that it is possible for a cubic function graph to have no turning point

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1. How the values of a affecting the graph

2. The turning point of the graph

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I learnt that a cubic graph can have no turning points

I learnt how to differentiate between the different shapes of graphs and how the coefficient of each term would affect the intercepts if the graph.

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1. I learnt how a cubic graph would look like.

2. I learnt that it is possible for a cubic graph to not have any turning point.

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I learnt how to differentiate the different type of cubic graphs when a>0 and a<0. I also learnt how to apply other formulas into the graph (e.g. discriminant). I struggled to read the graph and understand it.

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I learnt :

how the graph will change when a is positive/negative

shape of graph based on a, b, c, d

Challenges: i am not used to this type of equation yet

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1. I learnt that positive and negative coefficient of x^3 can change the direction of the graph

2. I learnt that the graph becomes more steep when the coefficient of x^3 becomes more positive

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I learnt that a cubic function can have 2 to 3 turning points or none, with number of solutions ranging from 1 to 3.

I learnt the different types of functions including constant, cubic, linear, quadratic, exponential.

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I learnt that when a becomes more positive, the graph becomes steeper.

I learnt that the number of solutions ranges from 1 to 3.

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I have learnt identify the different graphs and how they affect each other whenever a coefficient is changed.

I have also learnt that it is possible for the cubic function to have no turning point

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I learnt that a cubic function can have three solutions for x

I learnt that it is possible for a cubic function to have no turning point

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1. The graph for cubic functions can have no turning points.

2. The number of solutions for ax^3+bx^2+c+d+0 ranges from 1 to 3

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1. I learnt that it is possible that graphs of cubic functions don’t have turning points

2. When a becomes positive in the graph of y=x^3, the 2 arms of the graph move closer to the y axis

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1. I learned how the graph changes from positive to negative

2. The range of number of solutions is 1-3

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I learnt that it is possible for the graph of a cubic function to have no turning points

I have also learnt that it is possible for a cubic function to have 3 solutions (3 x-intercepts)

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I have learnt that cubic functions are able to have up to 3 solutions, ranging from 1-3

I have also learnt that the graph of the negative a-value would be reflected about the graph of the positive a-value

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i learnt that the difference between a<0 and a>0 is that the curves will be reflected

the range of solutions for cubic functions are from 1 to 3

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1)I learnt that it possible for a cubic function to have no turning point

2) sometimes the sketching of my graph is not good

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I have learnt that cubic functions do not always have to have a turning point

I have also learnt that the number of solutions of a cubic function ranges from 1 to 3.

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it is possible for the cubic function to have no turning point

i learnt that as the positive a becomes greater, the graph becomes steeper

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-It is possible for a cubic function graph to not have a turning point

-I have learnt that when a is positive the graph will start from the right of the y-axis while when a is negative the graph will start from the left of the y-axis

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i learnt that it is possible for a cubic function to have no turning points and it is possible for a cubic function to have 1-3 solutions

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A cubic function graph can have no turning points.

The maximum number of turning points a cubic function graph can have is 2.