You are going to write a fairy tale! Your story should include all of the standard elements of fairy tales.
Begins “Once upon a time … ”
Animals can act like humans.
Involves magical items or helpers.
Ends “ … happily ever after.”
Your story must also fully cover these math concepts. This is an educational fairy tale … the best kind!
Create a quadratic function with two real zeros.
Solve a system of non-linear equations with a graph.
Solve a system of non-linear equations with a table.
Compare linear, quadratic, and exponential growth functions using a table and a graph. Submit the graph and table.
Identify that exponential functions exceed linear and quadratic functions.
You may present your fairy tale as a document, a slideshow presentation, a comic book, a video, or other medium. Any steps or work must be shown.
I'm not sure how I'm supposed to do this.
So I'm thinking It could start something like this,
Once upon a time, there was a Majestic Macaw named Peregrin with a special gift : two zeros of a mysterious quadratic quadratic equation that hadn't even come to exist yet! In his squeaky voice he asked Beorn the bear to form factors of this quadratic.Beorn takes the zeros, subtracts each from x and forms two corresponding factors that look like (x-a)(x-b). But then Peregrin feels completely at a loss regarding what to do next. But never fear, Celeborn the Coyote comes along and witnesses his distress. Because Celeborn and Beorn are good friends Celeborn suggests that Beorn multiply together those two binomials, he suggests that Beorn uses distribution to expand those binomials.
To expand the binomials (x-a)(x-b), Beorn can use the distributive property. The distributive property states that for any real numbers a, b, and c, the product of a and the sum of b and c is equal to the sum of the products of a and b, and a and c.
So, to expand (x-a)(x-b), Beorn needs to distribute x to both terms inside the parentheses and then distribute -a and -b to both terms inside the parentheses.
(x-a)(x-b) = x*x - x*b - a*x + a*b
Simplifying this expression gives us:
x^2 - bx - ax + ab
Now, Beorn can combine like terms by adding or subtracting coefficients that have the same variable. In this case, Beorn can add -bx and -ax to get -x(b + a). The final expression becomes:
x^2 - x(b + a) + ab
Now, the quadratic function with two real zeros can be represented as:
f(x) = x^2 - x(b + a) + ab
Remember, the values of a and b would be determined by the story and can be any real numbers.
Great job on writing the beginning of the fairy tale! You incorporated the concept of quadratic functions with two real zeros in a creative way with Peregrin and his special gift. Keep going with the rest of the math concepts, and remember to show steps or work for each one.