Math I
Quadratic Applications
Name ________________________________
Date _________________________________
1. The distance of a diver above the water d (t ) (in feet) t seconds after diving off a platform is modeled by the equation
d (t )  16t 2  8t  30 . Find the time it will take for the diver to hit the water. Find the maximum height of the diver during
his dive.
2. The height h of a baseball t seconds after being hit is given by h(t )  16t 2  80t  3 . What is the maximum height that
the baseball reaches, and when does this occur?
3. A volcanic eruption blasts a boulder upward with an initial velocity of 240 feet per second. The equation
h(t )  240t  16t 2 represents this situation. How long will it take the boulder to hit the ground?
4. Marta throws a baseball with an initial velocity of 60 feet per second. Ignoring Marta’s height how long after she releases
the ball will it hit the ground if the equation h(t )  60t  16t 2 represents the situation?
5. The height h(t ) in feet of an object t seconds after it is propelled straight up from the ground with initial velocity of 60 feet
per second is modeled by the equation h(t )  16t 2  60t . At what height will the object be at 2 seconds after it is propelled
off of the ground?
Solve each equation by the method given.
6. Factoring. 2𝑥 2 − 7𝑥 = 4
7. Graphing. 6𝑥 2 + 𝑥 − 1 = 0
8. Quadratic Formula. 2𝑥 2 − 5𝑥 − 3 = 0
9. Completing the Square. 𝑥 2 + 4𝑥 = 5
Graph and find the following of each function.
1. 𝑦 = −3𝑥 2 − 18𝑥 + 2
a. axis of symmetry: ________
b. vertex: ________
c. y-intercept: ________
d. direction of opening: ________
e. domain: ______________
f. range: __________
g. x-intercepts
Math I
Quadratic Applications
Name ________________________________
Date _________________________________
1. The distance of a diver above the water d (t ) (in feet) t seconds after diving off a platform is modeled by the equation
d (t )  16t 2  8t  30 . Find the time it will take for the diver to hit the water. Find the maximum height of the diver during
his dive.
2. The height h of a baseball t seconds after being hit is given by h(t )  16t 2  80t  3 . What is the maximum height that
the baseball reaches, and when does this occur?
3. A volcanic eruption blasts a boulder upward with an initial velocity of 240 feet per second. The equation
h(t )  240t  16t 2 represents this situation. How long will it take the boulder to hit the ground?
4. Marta throws a baseball with an initial velocity of 60 feet per second. Ignoring Marta’s height how long after she releases
the ball will it hit the ground if the equation h(t )  60t  16t 2 represents the situation?
5. The height h(t ) in feet of an object t seconds after it is propelled straight up from the ground with initial velocity of 60 feet
per second is modeled by the equation h(t )  16t 2  60t . At what height will the object be at 2 seconds after it is propelled
off of the ground?
Solve each equation by the method given.
6. Factoring. 2𝑥 2 − 7𝑥 = 4
7. Graphing. 6𝑥 2 + 𝑥 − 1 = 0
8. Quadratic Formula. 2𝑥 2 − 5𝑥 − 3 = 0
9. Completing the Square. 𝑥 2 + 4𝑥 = 5
Graph and find the following of each function.
1. 𝑦 = −3𝑥 2 − 18𝑥 + 2
a. axis of symmetry: ________
b. vertex: ________
c. y-intercept: ________
d. direction of opening: ________
e. domain: ______________
f. range: __________
g. x-intercepts