Parábola or quadratic functions

Secondary. Age 15-16 years.
An 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:

 a) $y = x^2-5x+6$ b) $y=-x^2-4x-4$ 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) $x^2-5x+6=0$
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

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