Quadratic Function
The equation of a quadratic function is:
y = ax² + bx +c
Its graph is a parabola.
Graphical Representation of the Parabola
A parabola can be built from these points:
1. Vertex
The axis of symmetry passes through the vertex of the parabola.
The equation of the axis of symmetry is:
2. x-intercepts
For the intercept with the x-axis, the second coordinate is always zero:
ax² + bx +c = 0
To find the x-intecepts, solve the resultant quadratic equation:
Two intercept points: (x1, 0) (x2, 0) if b² − 4ac > 0
One intercept point: (x1, 0) if b² − 4ac = 0
No intercept points if b² − 4ac < 0
3. y-intercept
For the intercept with the y-axis, the first coordinate is always zero:
f(0) = a · 0² + b · 0 + c = c (0, c)
Example
Graph the quadratic function y = x² − 4x + 3.
1. Vertex
xv = − (−4)/2 = 2 yv = 2² − 4 · 2 + 3 = −1
V(2, −1)
2. x-intercepts
x² - 4x + 3 = 0
(3, 0) (1, 0)
3. y-intercept
(0, 3)
