Page 691 - Algebra 1

INVESTIGATION 10
Transforming Quadratic Functions
A quadratic function is a function that can be written in the form f(x) = ax2 + bx + c, where a is not equal to 0.
In Investigation 6, linear functions were graphed as transformations of the parent function f(x) = x. Similarly, you can graph a quadratic function as a transformation of the quadratic parent function f(x) = x2.
Parameter Changes
Complete the table of values for f(x) = x2 and graph the quadratic parent function.
x
-3
-2
f (x)
-1
0
1
2
3
Math Reasoning
Analyze If a = 0, would the function still be quadratic? If not, what type of function would f(x) be?
Online Connection www.SaxonMathResources.com
6. Predict How will the graph of f(x) = -4x2 change in relation to the quadratic parent function?
The graph of a function of the form f(x) = ax2 always crosses the y-axis at (0, 0). When c ≠ 0, the graph of the function f(x) = ax2 + c does not pass through the point (0, 0).
7. Graph the quadratic parent function and the function f(x) = x2 + 1 on the same set of axes. Compare the two graphs.
8. Graph the quadratic parent function and the function f(x) = x2 - 2 on the same set of axes.
As is the case for the linear parent function, the quadratic parent function f(x) = x2 can be written as f(x) = ax2, where a = 1. The graph changes when other values are substituted for a.
1. Graphy=x2 andy=2x2 onthesamesetofaxes.Comparethe two graphs.
2. Graph y = x2 and y = _1x2 on the same set of axes. Compare the 2
two graphs.
3. Graphy=x2 andy=-x2 onthesamesetofaxes.Comparethe two graphs.
4. Generalize What is the effect of a on the graph of y = ax2?
5. Predict How will the graph of f(x) = _2 x2 change in relation to the
quadratic parent function?
3
676 Saxon Algebra 1