Introduction
Have you ever wondered how to determine how long it will take a cannon ball to hit its target? A cannon shoots in a projectile motion that creates the same curve as a quadratic function. We can use the properties of a quadratic function to answer this question.
An object is launched from a 78.4-meter tall platform. The equation for the object's height s at time t seconds after launch is s(t) = −4.9t2 + 29.4+ 78.4, where s is in meters. When does the object strike the ground?
Go to Geogebra to find the time it takes for the object to hit the ground.
The x-axis will represent the ground. What are the two x-intercepts?
Can time be negative?
So, the object strikes the ground eight seconds after launch.
We can also solve this by factoring if you can remember from Algebra I:
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0 = −4.9t2 + 29.4t + 78.4 Factor out a gcf of −4.9
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0 = −4.9(t2 − 6t − 16) Now find the factors of −16 that add to equal −6.
0 = (t − 8)(t + 2) Now set each factor equal to zero and solve.
Then t = 8 or t = −2. In this lesson, we will look at solving quadratic equations by factoring.
Following successful completion of this lesson, students will be able to...
- Extend polynomial identities to the complex numbers.
- Interpret parts of an expression such as terms, factors, and coefficients.
- Use the structure of an expression to identify ways to rewrite it.
- Identify zeros of polynomials when suitable factorizations are available.
Essential Questions
- How do you find the zeros of a function?
- Why are some solutions extraneous or complex?
- How can you use functions to model real life problems?
Enduring Understandings
- Student understand the origin of complex numbers and how to manipulate them.
- Student understand the properties of and how to solve equations involving the different families of functions.
The above objectives correspond with the Alabama Course of Study Algebra II with Statistics standards: 1, 6, 11, and 12.