University:
High School
Course:
High School Mathematics
Academic year:

2023
Views:

285

Pages:

2
Author:

plongeq4

**2.2 Characteristics of Quadratics** **Modeling with Quadratics** **Examples** **1.** The parabola shows the path of your first golf shot, where x is the horizontal distance (in yards) and y is the corresponding height (in yards). The path of your second shot can be modeled by the function f(x) = -0.02x(x-80). Which shot travels farther before hitting the ground? Which travels higher? **1st Shot:** Traveled 100 yards and reached 25 yards in height **Intercept Form** f(x) = a(x-p)(x-q) p, q are the x-intercepts f(x) = -0.02x(x-80) = -0.02(x-0)(x-80) **X-intercepts:** 0 and 80 **2nd Shot:** Traveled 80 yards and reached a height of 32 yards **Find vertex to determine height** (40, ?) ⇒ (40, 32) height = y = -.02(40)(40-80) = -.02(40)(-40) height = 32 **1st shot traveled farther.** **2nd shot reached a higher height.** **2. A softball player hits a ball whose path is modeled by f(x) = -0.0005x² + 0.2127x + 3, where x is the distance from home plate (in feet) and y is the height of the ball above the ground (in feet). What is the highest point this ball will reach? If the ball was hit to center field which has an 8 foot fence located 410 feet from home plate, was this hit a home run?** **Standard Form** **Vertex = highest point** x = -b/2a = -0.2127 / 2(-0.0005) = -0.2127 / -0.001 = 212.7 y = -0.0005(212.7)² + 0.2127(212.7) + 3 = -0.0005(45241.29) + 45.241 + 3 = -22.62 + 45.241 + 3 = 25.62 (212.7, 25.62) Maximum height the ball reached. **25.62 feet** 25.6 HOME 212.7 410 425.4 PLATE height = y = -0.0005(410)² + 0.2127(410) + 3 = 6.157 approximately 6 feet **The hit was not a home run because at 410 feet, the height is about 6 feet which is less than the height of the fence.**