Funciones cuadráticas
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This document contains 5 quadratic functions and their domain, range, and intercepts. Each function is of the form y=ax^2+bx+c. The domain for each is R and the range is calculated and intercepts found by setting x=0 and y=0.
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Funciones cuadráticas
- 2. 1. Y=x²-5x+6 DomY= R RanY= 5/2=2.5 (2.5,-0.2) (2.5)²-5(2.5)+6=-0.2 RanY=(-0.2,+∞) Interceptos • Con x= Y=x²-5x+6 0=x²-5x+6 (x-3)(x-2) (3,0) (2,0) • Con y= Y=x²-5x+6 y=6 (0,6)
- 3. 2. Y=x²-3x+2 DomY= R RanY= 3/2=1.5 (1.5,-0.2) (1.5)²-3(1.5)+2= -0.2 RanY= (-0.2,+∞) Interceptos • Conx= Y=x²-3x+2 0=x²-3x+2 (x-2)(x-1) (2,0) (1,0) • Cony= Y=x²-3x+2 y=2 (0,2)
- 4. 3. Y=x²+2x-8 DomY= R RanY=-2/2=-1 (-1,-9) (-1)²+2(-1)-8=-9 RanY==(-9,+∞) Interceptos • Conx= Y=x²+2x-8 0=x²+2x-8 (x+4)(x-2) (-4,0) (2,0) • Cony= y=x²+2x-8 y=-8 (0,-8)
- 5. 4. Y=x²-4x+3 DomY= R RanY=4/2=2 (2,-1) (2)²-4(2)+3=-1 RanY=(-1,+∞) Interceptos • Conx= Y=x²-4x+3 0=x²-4x+3 (x-3)(x-1) (3,0)(1,0) • Cony= Y=x²-4x+3 y=3 (0,3)
- 6. 5. Y=x²-7x-18 DomY=∞ RanY=7/2=3.5 (3.5,-30.2) (3.5)²-7(3.5)-18=-30.2 RanY=(-30.2,+∞) Interceptos • Conx= Y=x²-7x-18 0=x²-7x-18 (x-9)(x+2) (9,0) (-2,0) • Cony= y=x²-7x-18 y=-18 (0,-18)