Graphing quadratic functions. Parabolas (ENG)

Parábola or quadratic functions

Secondary. Age 15-16 years.
mujer leyendoAn expression of type

y=ax^2+bx+c where a, b ,c \in \mathbb{R} with a \neq 0

quadratic function is called and is represented in parables.

If a>0, the branches of the parabola going up.
If a<0, the branches of the parabola going down.

The vertex is the point of V \left( - \dfrac{b}{2a} , - \dfrac{b^2-4ac}{4a} \right) and has a vertical axis of symmetry of equation x = - \dfrac{b}{2a}

The cuts to the axes are obtained by finding (0, c) for cutting with axis Y, and solve equation ax^2+bx+c=0 for the possible cutting with axis X (and second coordinate 0).

Optionally you can make a small table of values for complete information.

Example

1 .- Represented graphically, obtaining the elements of the parabola:

parabola-01
a) y = x^2-5x+6
parabola-02
b) y=-x^2-4x-4
parabola-03
c) y= x^2+1

Exercise

  1. Represented graphically the next parabolas .
    • y=x^2-4x+5
    • y=x^2/4-2x+3
    • y=2x^2-12x+10
  2. Solve the following quadratic equations by applying the formula for solving quadratic equations:

a) ecuations and coffeex^2-5x+6=0
b) x^2-x-6=0
c) 3x^2+9x-30=0
d) x^2-36=0
e) -x^2-2x+35=0

Sol: a) 2 y 3 b) 3 y -2 c) -5 y 2 d) -6 y 6 e) -7 y 5

You may be interested in this … VIDEO Second degree equations solved

Note: Maybe, you could help me to improved this traduction. I expect this exercise like you. Thanks.

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