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**Unformatted text preview: **Factors and x-intercepts An important relationship between an algebraic formula and the graph of the corresponding function is the following: If k is a real number, then (x k)- is a factor of function f k is an x-intercept of the graph of f. For example, the graph of the linear function y x 1 = - = - = - = - is a straight line that has the point (1, 0) as its x-intercept, and the graph of y x 3 = + = + = + = + has x-intercept at (-3, 0) . Also, the graph of the quadratic function y a(x 3)(x 1) = +- = +- = +- = +- is a parabola with x-intercepts at (-3, 0) and (1, 0) , with different values for the coefficient a resulting narrower or wider graphs depending upon the magnitude of a , opening upward or downward depending upon the sign of a . Examples : Draw graphs for the following third degree polynomials. 1) 3 y (x 3)(x 1)(x 2) x ..... 6 = +-- = + + = +-- = + + = +-- = + + = +-- = + + 2) 3 y (x 3)(x 1)(x 2) x ..... 6 = - +-- = - +- = - +-- = - +- = - +-- = - +- = - +-- = - +- 3) 3 y 2(x...

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