8/18/2019 Ejercicios Resueltos de La Función Cuadrática

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Ejercicios de la función cuadrática

Problemas   Soluciones

Representa las funciones cuadráticas

1   y = −x² + 4x − 3

2   y = x² + 2x + 1

3   y = x² + x + 1

4   Halla el vértice y la ecuación del eje de simetría de las siguientes parábolas:

1  y = (x − 1)² + 1

2   y = 3(x − 1)² + 1

3  y = 2(x + 1)² - 3

4  y = -3(x − 2)² − 5

5  y = x² − 7x − 18

6  y = 3x² + 12x − 5

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8/18/2019 Ejercicios Resueltos de La Función Cuadrática

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5   Indica, sin dibujarlas, en cuantos puntos cortan al eje de abscisas las siguientes

parábolas:

1  y = x² − 5x + 3

2   y = 2x² − 5x + 4

3  y = x² − 2x + 4

4  y = −x² − x + 3

6   Una función cuadrática tiene una expresión de la forma y = x² + ax + a y pasa por

el punto (1, 9). Calcular el valor de a.

7   Se sabe que la función cuadrática de ecuación y = ax² + bx + c pasa por los puntos

(1,1), (0, 0) y (-1,1). Calcula a, b y c.

8   Una parábola tiene su vértice en el pun to V(1, 1) y pasa por el pu nto (0, 2). Halla su

ecuación.

9   Partiendo de la gráfica de la función f(x) = x2, representa:

1   y = x² + 2

2   y = x² − 2

3  y = (x + 2)²

4  y = (x − 2)²

5  y = (x − 2)² + 2

6  y = (x + 2)² − 2

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