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By Gloria Grazioli Parabola

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Parabola

By Gloria Grazioli

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definition

A perfect parabola is a curve where the distance between a fixed point and another fixed line is the same at all points on the curve. The fixed point is called the focus and the fixed line is called the directrix.

(3)

How to graph a parabola

The graph of a quadratica equation with the form

y=ax

2

+bx+c

is a parabola.

If a>0 graph of y=ax

2

+bx+c forms a parabola that is

concave up

(4)

How to graph a parabola

The graph of a quadratica equation with the form y=ax

2

+bx+c

is a parabola.

If a<0 graph of y=ax

2

+bx+c forms a parabola that is

concave down

(5)

How to determine vertex

In order to determine the location of focus and directrix of the parabola, one needs to follow the following steps:

First the given equation of parabola is to be converted in the standard form of parabola

y=ax2+bx+c Find the vertex of the given parabola

𝑉(− 𝑏

2𝑎 ; − 𝑏2 − 4𝑎𝑐

4𝑎 )

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How to determine focus and directrix

Find the focus of the given parabola 𝐹(− 𝑏

2𝑎 ; − 𝑏2 − 4𝑎𝑐 − 1

4𝑎 )

Find the directrix of the given parabola

𝑦 = − 𝑏2 − 4𝑎𝑐 + 1 4𝑎

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Sketching Parabola

1. Find the vertex

2. Find the intercept (0;f(0))

3. Solve f(x)=0 to find the x coordinates of the x-intercepts (if they exixt)

4. Make sure that you’ve got at least one point to either side of the vertex (you can use the y-intercept and the axis of symmetry to get the second point)

5. Sketch the graph

Riferimenti

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