1. 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.

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

3. 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

4. Ex 1 Determine the type & number of solutions.

5. Ex 2 Determine the type & number of solutions.

6. 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?

7. Ex 4 Solve using the QF

8. Ex 5 Solve using the QF

9. 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)