Calculus – Quadratic Equations Practice Set · 4

Question:
A particle moves along a straight line so that its position at time t greater than or equal to 0 is given by s of t equals negative t squared plus 8t minus 7, in metres. At what time t does the particle first reach a position of s equals 9 metres?

Calculus – Quadratic Equations Practice Set · 4

This lesson explores how to find the time at which a particle reaches a specific position along a straight line, given a quadratic position function. Students set up and solve a quadratic equation, interpret a double root geometrically, and verify the answer by substitution.

In this lesson, you will learn to:
• Set up an equation by substituting a target position value into a quadratic position function
• Rearrange and solve a quadratic equation by factoring a perfect-square trinomial
• Interpret a double root as the parabola being tangent to a horizontal line
• Verify a solution by s