Drawing the graphs of functions y = mx + n

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The simplest way to draw the graph of a linear function is to use values from a

Drawing the graphs of functions y = mx + n

The simplest way to draw the graph of a linear function is to use values from a table of values. You should use values that are easy to calculate and, in the interest of drawing accuracy, values that are not too close together.

Determining the zero point

To determine the zero of a linear function - homework help geometry , substitute in the function equation for y = 0 and solve the resulting equation of determination for x.

Quadratic Functions

A function with an equation of the form

 y=f(x)=ax2+bx+c (with a≠0, x∈R)

or an equation that can be transformed into this form by equivalent transformation is called a quadratic function.

Here ax2 is called the quadratic term, bx the linear term and c the absolute term of the function equation.

The graph of a quadratic function is a parabola.

If we assume for the sake of simplicity that a bungee jumper falls freely from a height of h0 metres in the first phase after his jump, then according to the laws of physics he would find himself after t seconds at a height of

 h=h0-g2⋅t2 (g=9.81 ms2)

above the surface of the earth.

The equation

 h(t)=h0-g2⋅t2

describes a special quadratic function.

Definition: A function with an equation of the form

 y=f(x)=ax2+bx+c (with a≠0, x∈R)

or an equation that can be transformed into this form by equivalent transformations is called a quadratic function. (ax2 is called the quadratic term, bx the linear term and c the absolute term of the function equation).

The graph of a quadratic function is a parabola (quadratic parabola). The axis of symmetry of the parabola is parallel to the y-axis and intersects the graph of the function at the vertex (apex) of the parabola.

For a 0 the parabola is open upwards and for a 0 it is open downwards.

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