The document discusses the characteristics of quadratic equations, specifically how to identify and find the vertex, axis of symmetry, and minimum values. It explains the process of calculating the y-intercept from the c coefficient and provides examples using formulas to determine the line of symmetry and vertex coordinates. The document includes step-by-step instructions for solving specific quadratic equations to illustrate these concepts.

1. CHARACTERISTICS OF
QUADRATIC EQUATIONS

2.  The vertex is the point of the curve, where the line of
symmetry crosses.
 On the graph, the vertex is shown
by the arrow.
The co-ordinates of this vertex is
(1,-3)
 The vertex is also called the
turning point.
HOW TO FIND THE VERTEX

3.  To find the Y-intercept, you look and the C coefficient of the
quadratic equation.
 For example, if the quadratic equation is 5x2 + 3x -2, the Y-
intercept here is -2 because this is the C coefficient in the
quadratic equation.
HOW TO CALCULATE THE Y-INTERCEPT
C value

4.  Every parabola has an axis of symmetry. This line passes through the
vertex and divides the parabola into two halves that are mirror images.
 To find the Line of Symmetry of a quadratic equation (parabola), you
use the formula; x= -b/2a
 For example; Find the line of symmetry
(or axis of symmetry) for y = x2 – x -9
 Find the coefficients of A and B and plug them
into the formula A=1, B=-1
X= -b/2a
X= -(-1)/2(1)
X=1/2
X=0.5  The answer must include x= (so answer is x=0.5)
HOW TO CALCULATE THE LINE OF
SYMMETRY

5.  Question: Find the minimum value of y= x2 +6x +10
 To find the minimum value, first identify the A and B
coefficients. (A=1, B=6).
 Use the equation X=-b/2a and plug in the coefficients of A and B.
X=-(6)/2(1)
X=-6/2
X=-3
 Then plug the answer (the X value) into the original parabola to
find the minimum value.
X2 + 6x + 10
(-3)2 + 6(-3) + 10
9-18+10=1
HOW TO CALCULATE THE MINIMUM VALUE

6.  Question: Find the vertex (turning point) of y= 3x2 + 12x – 12
 First identify the coefficients of A and B (A=3, B=12) and plug
them into this equation; x=-b/2a
X=-(12)/2(3)
X=-12/6
X=-2  so this is the x-coordinate of the vertex
 Then plug that value of X into the original parabola:
3(-2)2 + 12(-2) – 12
12 – 24 – 12 = -24  this is the y-coordinate of the vertex
 So the vertex (turning point of this parabola is (-2,-24)
HOW TO CALCULATE THE VERTEX (TURNING
POINT)