Every cubic polynomial can be categorised into one of four types: Type 1: Three real, distinct zeros: P(x)=a(x−α)(x−β)(x−γ),a≠0 Type 2: Two real zeros, one repeated: P(x)=a(x−α)2(x−β),a≠0 Type 3: One real zero repeated three times: P(x)=a(x−α)3,a≠0 Type 4: One real and two imaginary zeros: P(x)=(x−α)(ax2+bx+c),Δ=b2−4ac&lt;0,a≠0 Experiment with the graphs of Type 1 cubics. Clearly state the effect of changing both the size and sign of a. What is the geometrical significance of α,β,and γ?α,β,and γ?

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Every cubic polynomial can be categorised into one of four types: Type 1: Three real, distinct zeros: P(x)=a(x−α)(x−β)(x−γ),a≠0 Type 2: Two real zeros, one repeated: P(x)=a(x−α)2(x−β),a≠0 Type 3: One real zero repeated three times: P(x)=a(x−α)3,a≠0 Type 4: One real and two imaginary zeros: P(x)=(x−α)(ax2+bx+c),Δ=b2−4ac&amp;lt;0,a≠0 Experiment with the graphs of Type 1 cubics. Clearly state the effect of changing both the size and sign of a. What is the geometrical significance of α,β,and γ?α,β,and γ?

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The size of ¢ controls the vertical stretch or shrink of the graph Changing the sign of « reflects the graph about x-axis&amp;nbsp;α−β&amp;nbsp;and&amp;nbsp;γ&amp;nbsp;are the x-intercepts of the graph.

Every cubic polynomial can be categorised into one of four types: Type 1: Three real, distinct zeros: P(x)=a(x−α)(x−β)(x−γ),a≠0 Type 2: Two real zeros

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