Examine the graph below.
![GRAPH OF A PARABOLA THAT OPENS UPWARD WITH A \(y\)-intercepts OF NEGATIVE 3 AND \(x\)-intercepts OF NEGATIVE 1 AND 3.]()
Which function matches the graph?
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Match Quadratic Graphs and Their Equations
The factored form helps find the zeros of a quadratic function.
The factored form gives the zeros, and the -intercepts are located where each factor equals 0.
Example
Examine the graph. What are the -intercepts of the graph?
The graph crosses the -axis at and . These are the -intercepts.
Look at each function to see which matches the graph. Look for the factors that have zeros as and .
a.
- This function has zeros at and . The zero is not a zero on the graph.
b.
- This function has zeros at and . The zero is not a zero on the graph.
c.
- This function has zeros at and . The signs of the zeros of this function are the opposite of the signs of the zeros on the graph.
d.
- This function has zeros at and . This function has zeros that match the zeros on the graph.
The function matches the graph.
Try It: Match Quadratic Graphs and Their Equations
Examine the graph.
Which function matches the graph?
a.
b.
c.
d.
Here’s how to match the function to the graph.
Look at each function to see which matches the graph. Look for the factors that have zeros at and .
- This function has zeros at and . The zero is not a zero on the graph.
- This function has zeros at and . The zero is not a zero on the graph.
- This function has zeros at and . This function has zeros that match the zeros on the graph.
- This function has zeros at and . The zeros of the function have the opposite signs of the zeros on the graph.
The function matches the graph.
Check Your Understanding
Examine the graph.
Which function matches the graph?
Multiple Choice: