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Algebra 1

Match Quadratic Graphs and Their Equations: Mini-Lesson Review

Algebra 1Match Quadratic Graphs and Their Equations: Mini-Lesson Review

Match Quadratic Graphs and Their Equations: Mini-Lesson Review

Match Quadratic Graphs and Their Equations: Mini-Lesson Review

Mini Lesson Question

Question #3: Match Quadratic Graphs and Their Equations

Examine the graph below.

Which function matches the graph?

  1. f ( x ) = ( x + 1 ) ( x + 3 )
  2. f ( x ) = ( x − 1 ) ( x − 3 )
  3. f ( x ) = ( x + 1 ) ( x − 3 )
  4. f ( x ) = ( x − 1 ) ( x + 3 )

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 x x -intercepts are located where each factor equals 0.

Example

Examine the graph. What are the x x -intercepts of the graph?

The graph crosses the x x -axis at x = − 4 x = − 4 and x = 1 x = 1 . These are the x x -intercepts.

Look at each function to see which matches the graph. Look for the factors that have zeros as x = − 4 x = − 4 and x = 1 x = 1 .

a. f ( x ) = ( x + 4 ) ( x + 1 ) f ( x ) = ( x + 4 ) ( x + 1 )

  • This function has zeros at x = − 4 x = − 4 and x = − 1 x = − 1 . The zero x = − 1 x = − 1 is not a zero on the graph.

b. f ( x ) = ( x − 4 ) ( x − 1 ) f ( x ) = ( x − 4 ) ( x − 1 )

  • This function has zeros at x = 4 x = 4 and x = 1 x = 1 . The zero x = 4 x = 4 is not a zero on the graph.

c. f ( x ) = ( x − 4 ) ( x + 1 ) f ( x ) = ( x − 4 ) ( x + 1 )

  • This function has zeros at x = 4 x = 4 and x = − 1 x = − 1 . The signs of the zeros of this function are the opposite of the signs of the zeros on the graph.

d. f ( x ) = ( x + 4 ) ( x − 1 ) f ( x ) = ( x + 4 ) ( x − 1 )

  • This function has zeros at x = − 4 x = − 4 and x = − 1 x = − 1 . This function has zeros that match the zeros on the graph.

The function f ( x ) = ( x + 4 ) ( x − 1 ) f ( x ) = ( x + 4 ) ( x − 1 ) matches the graph.

Try it

Match Quadratic Graphs and Their Equations

Examine the graph.

Which function matches the graph?

a. f ( x ) = ( x + 2 ) ( x + 4 ) f ( x ) = ( x + 2 ) ( x + 4 )

b. f ( x ) = ( x − 2 ) ( x − 4 ) f ( x ) = ( x − 2 ) ( x − 4 )

c. f ( x ) = ( x + 2 ) ( x − 4 ) f ( x ) = ( x + 2 ) ( x − 4 )

d. f ( x ) = ( x − 2 ) ( x + 4 ) f ( x ) = ( x − 2 ) ( x + 4 )

Check Your Understanding

Examine the graph.

Which function matches the graph?

  1. f ( x ) = ( x − 3 ) ( x − 2 ) f ( x ) = ( x − 3 ) ( x − 2 )

  2. f ( x ) = ( x − 3 ) ( x + 2 ) f ( x ) = ( x − 3 ) ( x + 2 )

  3. f ( x ) = ( x + 3 ) ( x − 2 ) f ( x ) = ( x + 3 ) ( x − 2 )

  4. f ( x ) = ( x + 3 ) ( x + 2 ) f ( x ) = ( x + 3 ) ( x + 2 )

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