Solving+Quadratic+Equations+for+Real+World+Scenarios

b) Solve quadratic equations by inspection ( e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a __+__ bi for real numbers a and b. Questions that should prompt some discussion but not limited to: What is the ideal shape? (parabola) What equation represents this shape? y = ax2 + bx +c
 * Expressions and Equations**
 * Unit Goal**: Solve real world problems using quadratic equations.
 * Standard: A.REI.4** Solve quadratic equations in one variable.
 * Task part 1:**
 * Scenario**: You are the project manager for preparing the area for a football field.
 * Do you want to make this area perfectly flat? Why or Why not?
 * Since it is outside do you need to take weather, specifically rain, into consideration?
 * Do you want it to all slope one way? Why or Why not?
 * Does the slope need to be steep?

The ideal surface for a football field is a parabola, the cross section of a field with synthetic turf can be modeled by y = -0.000234(x-80)2 + 1.5 where x and y are measured in feet.(**Teacher note**: discuss the properties of the equation and why is the //a// negative etc.) From the given equation can you find the width of the field?
 * Task part 2:**


 * Task part 3:**
 * From the given equation what is the maximum height of the fields surface?
 * What part of the parabola does this represent?
 * How much higher is the field at the vertex than at the sidelines (lowest point)

Do you think this slope would be detectable by the players on the field?
 * Task part 4:**
 * Calculate the slope from the vertex to the sideline ( slope of the secant line).
 * How do you know if this is detectable by the players on the field?

Can you think of another place where a parabola may be used for the purpose of rain run-off?
 * Freeways