Assignment: Quadratic Equations, Graphs, and Discriminant Analysis

This assignment delves into the fundamentals of quadratic equations, beginning with the general form and the roles of constants and variables. It explores the graphing of parabolas, identifying the axis of symmetry and vertex, and how the constant 'c' affects the graph's vertical position. The assignment then moves on to solving quadratic equations, emphasizing the importance of setting the equation to zero and utilizing graphing techniques to find intercepts. The quadratic formula is introduced, and students are tasked with applying it to a specific equation, finding solutions in decimal form. The concept of the discriminant is explored, explaining how its value determines the nature of the roots (real, equal, or complex). Finally, the assignment covers how to find the vertex and the axis of symmetry, and the relationship between the graph and the quadratic equation.

1) Graph Basics
a)
The general form of quadratic equation is given by,
Where a,b,c are constants and x and y are variables.
b)
The line of symmetry of this parabola is y axis.
c)

The vertex of this parabola is (0,0)
d)
the constant c determines how vertical distance the parabola moves.
That is the distance that the vertex moves with respect to the y axis of the graph.
2)
a) Befrore solving a quadratic equation, you must make it equal to zero.
b)To solve a quadratic equation usinga graph find the intercepts.
c)
given,
y=
here a=2, b=4, c=-3
d)
= =0
=
=

=x= , -1-
That is x=0.58,-2.58
e)
discriminant, D=
=
i)
if the discriminant is positive, there will be 2 values for x and there fore two separate roots
ii)
if the discriminant is zero, there is only one value for x, but there are in fact two roots which are
equal.
iii)
if the discriminant is negative, there is no real value for x. The value for the roots is a complex
number.
3.
a)
For a quadratic equation in standard for, y= .
the axis of symmetry is a vertical line
b)the y cordinate of the vertex is found out by substituting the above value of x the general
quadratic equation.
That is,
=
=
Therefore the cordinates = (
c)
i)does the graph turn up or down
ii)find the vertex
iii)find the intercepts
iv)graph the parabola