1.7 The Graphs of Quadratic Functions

Question 1

What is the characteristic shape of a quadratic on a graph?

Answer 1

A parabola.

It has a minimum/maximum point - a vertex
(It has a line of symmetry)

Question 2

What method is there for finding the vertex and line of symmetry without plotting the points?

Answer 2

Completing the square.

Question 3

The process of completing the square for a graph.

y = x^2 - 4x + 5

Answer 3

y = x^2 - 4x + 5

Seperate the constant.
x^2 - 4x = y - 5

Take the coefficient of the middle term, halve it, and square the answer.
-4 becomes -2 becomes 4

Add this to both sides.
x^2 - 4x + 4 = y - 5 + 4
(x - 2)^2 = y - 1
(x - 2)^2 + 1 = y

The line of symmetry is:
x - 2 = 0
x = +2

The vertex is the end number:
therefore: (2, 1)