7.2/7.3 The Discriminant & Quadratic Formula Learning goal Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

If a quadratic equation is written in standard form then it can be solved with the Quadratic Formula

discriminant : value beneath the radical Value of Discriminant Number of Solutions Type of Solutions Graph Intercepts Graph > 0 and a perfect square 2 rational 2 x-intercepts and NOT a perfect square irrational = 0  1 1 x-intercept < 0 complex; no real no x-intercepts

Ex 1 Determine the type & number of solutions.

Ex 2 Determine the type & number of solutions.

Ex 3 A player throws a ball up and toward a wall that is 17 feet high. The height h in feet of the ball t seconds after it leaves the player’s hand is modeled by the equation above. If the ball makes it to wall, will it go over the wall or hit the wall?

Ex 4 Solve using the QF

Ex 5 Solve using the QF

Ex 6 A swimming pool 6 m wide and 10 m long is to be surrounded by a walk of uniform width. The area of the walk happens to be equal to the area of the pool. What is the width of the walk? (Hint: Draw a diagram 1st)