Vertex Form and Football Trajectory

The video tutorial explains a story problem where Laura kicks a football. It covers sketching the path of the football, understanding the graph, finding the vertex, deriving the quadratic equation, and solving for the 'a' value. The tutorial also uses Desmos to calculate the horizontal distance when the ball is 20 feet high.

What is the initial distance the football lands from Laura?

• 100 feet

• 30 feet

• 50 feet

• 80 feet

What is the maximum height reached by the football?

• 60 feet

• 50 feet

• 70 feet

• 80 feet

Where is Laura positioned on the graph?

• At (0,0)

• At (25,0)

• At (50,0)

• At (80,0)

What is the significance of the vertex in the graph?

• It is the midpoint of the football's path.

• It is the highest point the football reaches.

• It is the point where the football lands.

• It is the starting point of the football.

What is the x-coordinate of the vertex?

• 50

• 80

• 0

• 25

What is the vertex form of a quadratic equation?

• y = a(x - h)^2 + k

• y = ax^2 + bx + c

• y = a(x + h)^2 - k

• y = ax + b

What does the 'a' value in the vertex form represent?

• The horizontal shift

• The vertical shift

• The x-intercept

• The stretch or shrink factor

What is the value of 'a' in the equation derived?

• -80/625

• 80/625

• -625/80

• 625/80

What is the complete vertex form of the equation for the football's path?

• y = -80/625(x - 25)^2 + 80

• y = 80/625(x - 25)^2 + 80

• y = 80/625(x + 25)^2 - 80

• y = -80/625(x + 25)^2 - 80

What is the height of the football when it is 20 feet high?

• It never reaches 20 feet.

• It is 20 feet high only on the way down.

• It is 20 feet high only on the way up.

• It is 20 feet high on the way up and down.