CONVERT QUADRATIC FUNCTIONS FROM ONE FORM TO …

CONVERT QUADRATIC FUNCTIONS FROM ONE form TO ANOTHER (Standard form <==> Intercept form <==> vertex form ) (By Nghi H Nguyen Dec 08, 2014) 1. THE QUADRATIC FUNCTION IN INTERCEPT form The graph of the QUADRATIC function in standard form , f(x) = ax + bx + c, is a parabola that may intercept the x-axis at 2 points, unique point, or no point at all. This means a QUADRATIC equation f(x) = ax + bx + c = 0 may have 2 real roots, one double real root, or no real roots at all (complex roots). We can write f(x) in the form : y = a(x + bx/a + c/a) (1). Recall the development of the QUADRATIC formula: x + bx/a + (b /4a - b /4a ) + c/a = 0 (x + b/2a) - (b - 4ac)/4a = 0 (x + b/2a) - d /4a = 0.

Vertex form y = 2(x + 9/4)² - 1/8. NOTE. There is another method to convert y, from standard form to vertex form, by completing the squares. Both methods, using general expression or completing the squares, start from the same origin: the development of the quadratic formula. Example 4. Convert y = 5x² + 6x – 8 to vertex form. Solution.

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  Form, Vertex, Vertex form

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