How To Graph

1
How To Graph Quadratic Equations
2
Getting Started

• The standard form of a quadratic equation is y
  ax2 bx c.
• The graph of a quadratic equation is a parabola.
• When a is positive, the graph opens up.
• When a is negative, the graph opens down.
• Every parabola has a vertex. For graphs opening
  up, the vertex is a minimum (low point). For
  graphs opening down, the vertex is a maximum
  (high point).
• The x-coordinate of the vertex is equal to
  .

3
Find the Vertex
You are given the equation y-x2 4x 1. Find
the coordinates of the vertex.
The coordinates of the vertex are (2,3)
4
Table of Values

• Choose two values of x that are to the right or
  left of the x- coordinate of the vertex.
• Substitute those values in the equation and solve
  for y.
• Graph the points.
• Since a parabola is symmetric, you can plot those
  same y-values on the other side of the parabola,
  the same distance away from the vertex.

x
y -x2 4x -1
y
y -(1)2 4(1) - 1 y -1 4 - 1
1
2
y -(-1)2 4(-1) -1 y -1 -4 -1
-6
-1
5
Graph the Parabola
Plot the vertex and the points from your table of
values (2,3), (1,2), (-1,-6).
Since a parabola is symmetric and has a vertical
line of symmetry through the vertex of the
parabola, points which are the same distance to
the right of the vertex will also have the same
y-coordinate as those to the left of the vertex.
Therefore, we can plot points at (3,2) and (5,-6).
Sketch in the parabola.
6
You Try It
Find the vertex of the following quadratic
equations. Make a table of values and graph the
parabola.
7
Problem 1
y
x
The vertex is at (2,-4)
8
Problem 2
The vertex is at (0,3)
9
Problem 3
The vertex is at (3,-5)