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Algebra 1

7.17.3 Changing the Parameters of a Quadratic Expression

Algebra 17.17.3 Changing the Parameters of a Quadratic Expression

7.17.3 Changing the Parameters of a Quadratic Expression

7.17.3 • Changing the Parameters of a Quadratic Expression

Activity

Mai is learning to create computer animation by programming. In one part of her animation, she uses a quadratic function to model the path of the main character, an animated peanut, jumping over a wall.

Mai uses the equation f ( x ) = − 0.1 ( x − h ) 2 + k f ( x ) = − 0.1 ( x − h ) 2 + k to represent the path of the jump. f f represents the height of the peanut as a function of the horizontal distance it travels, x x .

On the screen, the base of the wall is located at ( 22 , 0 ) ( 22 , 0 ) , with the top of the wall at ( 22 , 4.5 ) ( 22 , 4.5 ) . The dashed curve in the picture shows the graph of one equation Mai tried, where the peanut fails to make it over the wall.

1.

What is the value of h h in this equation?

2.

What is the value of k k in this equation?

3.

Starting with Mai's equation, choose values for h h and k k that will guarantee the peanut stays on the screen but also makes it over the wall. Be prepared to explain your reasoning.

Video: Changing the Parameters of a Quadratic Expression

Watch the following video to learn more about changing the parameters of a quadratic expression.

Changing the Parameters of a Quadratic Expression

Self Check

Cash kicked a football off a tee. The path of the football is shown below and represented by the function f ( x ) = − 0 .02 ( x − h ) 2 + k , where x represents the horizontal distance and f ( x ) represents the height.

Find the vertex and its meaning.

  1. ( 30 , 0 ) , the football travels 30 feet before hitting the ground.
  2. ( 14 , 5 ) the football hit its highest height of 14 feet after traveling 5 feet.
  3. ( 14 , 5 ) , the football hit its highest height of 5 feet after traveling 14 feet.
  4. ( 0 , 1 ) , the ball was kicked from a height of 1 foot.

Additional Resources

Determining the Vertex From a Graph

Zaren made a paper football for a game at indoor recess and flicked it in the air from a table. The path of the paper football is shown below and represented by the function f ( x ) = − 0 .02 ( x − h ) 2 + k f ( x ) = − 0 .02 ( x − h ) 2 + k .

Find the value of the vertex and its meaning:

The peak of the graph is at ( 17 , 3 ) ( 17 , 3 ) . This means the maximum horizontal distance traveled was 17 inches when the height of the object was 3 inches.

Try it

Determining the Vertex From a Graph

The revenue made from a high school play is shown in the graph above. Find the vertex and tell what it means in this situation.

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