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The Number of Zeros of a Quadratic Relation

Source: Camping - Prostock-Studio/iStock/Getty Images 

The Number of Zeros

 

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Lesson Goals

  • Determine the number of zeros of a quadratic relation given its equation written in factored or vertex form.
  • Calculate the discriminant of a quadratic relation given in standard form and use it to determine the number of zeros of the relation.
  • Given a family of parabolas, determine which members of the family have \(0\), \(1\), or \(2\) zeros.

Try This

Did You Know?

When backcountry camping, it is necessary to hang food in a tree to keep it away from bears. One way to hang the food is to tie a rock to the end of a rope and then throw the rock over a thick branch that is well above the ground. When the rock comes down, the rope is looped around the tree branch. You can tie your bag of food to the end of the rope and then hoist it up away from the reach of bears.

A bag hung from a tree out of reach of a nearby bear.

Sources: Bear - bazzier/iStock/Getty Images; Camping Bag - Allevinatis/iStock/Getty Images; 
Forest - November_Seventeen/iStock/Getty Images

While backcountry camping, Mirabel throws a rock tied to a rope toward a branch that is \(5\) metres above the ground. The rock's flight is modeled by \(h=-4.9t^2+7t+2\) where \(h\) is the height of the rock above the ground (in metres), and \(t\) is the time (in seconds). Does the rock make it to the branch?

Math in Action

The equation \(h=-4.9t^2+7t+2\) describes the height of an object thrown upwards with an initial speed of \(7\) m/s and with starting height \(2\) m. The number \(-4.9\) is a constant quantifying the effect of gravity.