Chandler Harris
05/27/2023 · Junior High School
2) Hallor la forma polinómica, canónica y foctorizada de las siguientes funciones cuadráticos: a. El coeficiente principal es \( \frac{1}{4} \) y tiene raices en \( x=-2 y x-6 \). b. El coeficiente principal es -2 y tiene raices en \( x=-\frac{1}{2} y x-\frac{1}{4} \). c. El coeficiente principal es -1 y el vértice es \( (-2 ; 1) \). d. El coeficiente principal es \( \frac{2}{5} \) y el vértice es \( (3 ;-1) \).
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a. Forma polinómica: \( f(x) = \frac{1}{4}x^2 - \frac{1}{2}x - 3 \)
Forma canónica: \( f(x) = \frac{1}{4}(x+2)(x-6) \)
Forma factorizada: \( f(x) = \frac{1}{4}(x+2)(x-6) \)
b. Forma polinómica: \( f(x) = -2x^2 + x + \frac{1}{2} \)
Forma canónica: \( f(x) = -2\left(x+\frac{1}{2}\right)\left(x+\frac{1}{4}\right) \)
Forma factorizada: \( f(x) = -2\left(x+\frac{1}{2}\right)\left(x+\frac{1}{4}\right) \)
c. Forma polinómica: \( f(x) = -1(x+2)^2 + 1 \)
Forma canónica: \( f(x) = -(x+2)^2 + 1 \)
Forma factorizada: \( f(x) = -(x+2)^2 + 1 \)
d. Forma polinómica: \( f(x) = \frac{2}{5}(x-3)^2 - 1 \)
Forma canónica: \( f(x) = \frac{2}{5}(x-3)^2 - 1 \)
Forma factorizada: \( f(x) = \frac{2}{5}(x-3)^2 - 1 \)
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