QUADRATICS
MAKE SENSE
Word Problems
Tips/Hints
When the question is asking for the vertex - complete the square.
To find the x-intercepts - use the quadratic formula.
Example 1
A garden measuring 12 metres by 16 metres is to have a pedestrian pathway installed all around it, increasing the total area to 285 square metres. What will be the width of the pathway?
Example 2
The height of a coin in the air t seconds after it is flipped can be modeled by
y = -16t^2 + 32t + 5, where t and y are measured in m. What is the maximum height that the coin reaches?
->To solve this, we need to complete the square because it is asking for the maximum height (y value of the vertex).
y=(-16t^2 + 32t) + 5
y= -16(t^2 - 2) + 5
y= -16 (t^2 - 2 + 1) -1) +5 -> -16 multiplies with -1
y= -16 (t-1)^2 + 21
The vertex is (1,21). Therefore the maximum height of the coin is 21m.