Lesson: Applications of Quadratics

​Projectile motion is a commonly modeled by quadratic functions

​Applications of Quadratic Functions

y-intercept generally tells how high the object was initially
vertex x-coordinate tells WHEN the object reaches max height, y-oord IS max height
x-intercept tell us when the object is on the ground

When an object is thrown...

Multiple Choice

Which one are we looking for?

A rubber ball was thrown into the air, then hit the ground causing it to bounce. How long did it take to hit the ground?

• x at vertex

• y at vertex

• positive zero

• y-intercept

Multiple Choice

Which one are we looking for?

Jaiden wanted to know the initial height of a baseball when it was hit at home plate.

• x at vertex

• y at vertex

• positive zero

• y-intercept

Multiple Choice

Which one are we looking for?

Hailee bungee jumped off a platform by first jumping into the air, then falling downward. How high was the platform?

• x at vertex

• y at vertex

• positive zero

• y-intercept

Determine WHAT the question wants you to find.
Then use your math skills to find what you need. Graphing can be helpful for a visual.

​

​When solving word problems....

Multiple Choice

The parabola shows the trajectory of a tennis ball that was hit with a tennis racket. What is the starting height of the tennis ball? (Click the picture to enlarge it)

• 3 feet - y-intercept

• 12 feet - vertex

• 1.5 seconds - vertex

• 3 seconds - x-intercept

Multiple Choice

If I want to find out when an object hits the ground, I should _________.

• Use x = (-b/2a) as my answer.
• Set my equation = 0 and solve.
• Replace x with 0 and evaluate.
• Find the y-coordinate of the vertex.

Multiple Choice

If I want to see the initial height of an object, I should _____________.

• Substitute x = 0 into the equation and evaluate.
• Use x = (-b /2a) as my answer.
• Find the y-coordinate of the vertex. 
• Set my equation = 0 and solve.

Multiple Choice

If you are given the zeros of a quadratic function, what is the easiest way to find the axis of symmetry?

• you don't have enough information

• guess and check with a graph until you find the x-intercepts that match

• find the middle number between the zeros

Multiple Choice

The parabola shows the trajectory of a tennis ball that was hit with a tennis racket. How long di it take for the tennis ball to hit the ground? (Click the picture to enlarge it)

• 3 feet

• 12 feet

• 1.5 seconds

• 3 seconds

Multiple Choice

What is the highest point over the water?

• 8 meters

• 1 meter

• 1 second

• 8 seconds

Multiple Choice

How long did it take to reach highest point over the water?

• 8 meters

• 1 meter

• 1 second

• 8 seconds

Multiple Choice

Does this graph have a maximum or minimum?

• Minimum
• Maximum

Multiple Choice

At 6 seconds is the rocket going up or down?

• up

• down