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In this lesson, we will learn how to write a cubic equation given three x-intercepts and one point on the graph.

Q1:

The figure shows the curve π¦ = π₯ β 2 π₯ 3 together with the line π¦ = π ( π₯ β 1 ) β 1 which has slope π and passes through point ( 1 , β 1 ) .

Write a cubic polynomial whose roots are the numbers π , π , and 1.

Divide this polynomial by π₯ β 1 to get a quadratic that is a multiple of ( π₯ β π ) ( π₯ β π ) .

Since π > π , determine π in terms of π .

Imagine changing the value of the slope π so that the value of π gets closer and closer to 1. When π = 1 , the line will be tangent to the curve at the point ( β 1 , 1 ) . Determine the equation of the tangent to the curve at the point ( β 1 , 1 ) .

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