# Quadratic Graphs- Terminology

Revision notes on Quadratic Graphs for Edexcel AS Maths.

- Created by: Anonymous
- Created on: 15-10-07 11:01

First 228 words of the document:

Quadratic Graphs

y = x 2x15

2

The vertex The turning point

This can be the maximum or minimum point of the graph. It can be found either by

completing the square:

y = (x1)216

vertex = (1.16)

or by differentiating f(x), because the gradient at the vertex is 0 and then substituting the

value of x into the equation:

f'(x) = 2x2

2x2 = 0

x=1

y = 122x115 = 16

vertex = (1,16)

The tangent A line that touches the curve

A tangent has the same gradient as the curve at the point where it touches. The equation for

a tangent is found by differentiating f(x) to find the gradient of the curve, then substituting in

the xcoordinate of the point where the tangent touches the curve. This gives the gradient of

the tangent. Ex: (3,12)

f'(x) = 2x2

f' (3) = 4

y+12 = 4(x3)

The xintercepts The points where the curve crosses the xaxis

The xintercepts can be found by substituting y=0 into the equation and then solving the

equation to find the values of x:

x22x15 = 0

(x+3)(x5) = 0

x= 3 or 5

The yintercepts The point where the curve crosses the yaxis

This can be found by substituting x=0 into the equation to find the value of y

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