Beginning and Intermediate Algebra - Wallace Math Courses ...

9.11
Quadratics - Graphs of Quadratics
Objective: Graph quadratic equations using the vertex, x-intercepts,
and y-intercept.
Just as we drew pictures of the solutions for lines or linear equations, we can draw
a picture of solution to quadratics as well. One way we can do that is to make a
table of values.
Example 501.
y = x2 − 4x +3 Make a table of values
x y
0
1
We will test5values to get an idea of shape
2
3
4
y = (0) 2 +4(0)+3=0−0+3=3 Plug 0 in for x and evaluate
y =(1) 2 − 4(1)+3=1−4+3=0 Plug 1 in for x and evaluate
y = (2) 2 − 4(2)+3=4−8+3=−1 Plug 2 in for x and evaluate
y =(3) 2 − 4(3)+3=9−12 + 3=0 Plug 3 in for x and evaluate
y =(4) 2 − 4(4)+3=16 − 16 + 3=3 Plug 4 in for x and evaluate
x y
0 3
1 0
Our completed table. Plot points on graph
2 − 1
3 0
4 3
Plot the points (0, 3), (1, 0), (2, − 1),
(3, 0), and(4, 3).
Connect the dots with a smooth
curve.
Our Solution
When we have x 2 in our equations, the graph will no longer be a straight line.
Quadratics have a graph that looks like a U shape that is called a parabola.
World View Note: The first major female mathematician was Hypatia of Egypt
who was born around 370 AD. She studied conic sections. The parabola is one
type of conic section.
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