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Algebra 1

Find Intercepts: Mini-Lesson Review

Algebra 1Find Intercepts: Mini-Lesson Review

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Mini Lesson Question

What are the x -intercept(s) of the graph of y = ( 2 x 9 ) ( x + 2 ) ?
  1. x = 2 , x = 9
  2. x = 2 , x = 9
  3. x = 2 , x = 4.5
  4. x = 2 , x = 4.5

Find the x x -Intercepts

The x x -intercepts of the graph of an equation occur when y = 0 y = 0 .

Example 1

For the equation y = ( x 9 ) ( x + 2 ) y = ( x 9 ) ( x + 2 ) , look at the factors ( x 9 ) ( x 9 ) and ( x + 2 ) ( x + 2 ) .

Notice in the first factor, ( x 9 ) ( x 9 ) , x = 9 x = 9 makes the factor equal to 0.

Substitute 9 for x x in the equation.

y = ( 9 9 ) ( 9 + 2 ) y = ( 9 9 ) ( 9 + 2 )

y = ( 0 ) ( 11 ) y = ( 0 ) ( 11 )

y = 0 y = 0

Notice in the second factor, ( x + 2 ) ( x + 2 ) , x = 2 x = 2 makes the factor equal to 0.

Substitute -2 for x x in the equation.

y = ( 2 9 ) ( 2 + 2 ) y = ( 2 9 ) ( 2 + 2 )

y = ( 11 ) ( 0 ) y = ( 11 ) ( 0 )

y = 0 y = 0

In the equation y = ( x 9 ) ( x + 2 ) y = ( x 9 ) ( x + 2 ) , y = 0 y = 0 when x = 9 x = 9 and x = 2 x = 2 .

The x x -intercepts occur when x = 9 x = 9 and x = 2 x = 2 .

To find the x x -intercepts of a quadratic equation in factored form, set each factor equal to zero and solve for x x .

Example 2

Find the x x -intercepts for y = ( 2 x + 7 ) ( x 4 ) y = ( 2 x + 7 ) ( x 4 ) .

The x x -intercepts occur when y = 0 y = 0 .

Set each factor to 0 and solve.

2 x + 7 = 0 x 4 = 0 x = 3.5 x = 4 2 x + 7 = 0 x 4 = 0 x = 3.5 x = 4

Try it

Try It: Find the x x -Intercepts

Find the x x -intercepts for y = ( 2 x 5 ) ( x + 3 ) y = ( 2 x 5 ) ( x + 3 ) .

Check Your Understanding

What are the x x -intercept(s) of the graph of y = ( 2 x + 1 ) ( x 3 ) y = ( 2 x + 1 ) ( x 3 ) ?

Multiple Choice:

  1. x = 3 x = 3 , x = 0.5 x = 0.5

  2. x = 3 x = 3 , x = 0.5 x = 0.5

  3. x = 3 x = 3 , x = 1 x = 1

  4. x = 3 x = 3 , x = 1 x = 1

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