We previously learned how to solve any quadratic equation using the method known as: completing the square. We can use this process to create a general formula for solving any quadratic equation. This formula is known as the “Quadratic Formula”.
Test Objectives:•Demonstrate the ability to write a quadratic equation in standard form
•Demonstrate the ability to identify a, b, and c in a quadratic equation
•Demonstrate the ability to solve a quadratic equation using the quadratic formula
The Quadratic Formula Test:
#1:
Instructions: Solve each equation using the quadratic formula.
a) $$2x^2 + 11x + 12 = 0$$
#2:
Instructions: Solve each equation using the quadratic formula.
a) $$6n^2 - 10n + 7 = 0$$
#3:
Instructions: Solve each equation using the quadratic formula.
a) $$-10x^2 + 6 = 0$$
#4:
Instructions: Solve each equation using the quadratic formula.
a) $$7x^2 = -11 + 10x + 5x^2$$
#5:
Instructions: Solve each equation using the quadratic formula.
a) $$-p^2 - 10p - 25 = 0$$
Written Solutions:
Solution:
a) $$x = -\frac{3}{2}$$ or $$x = -4$$
Solution:
a) no real solution
Solution:
a) $$x = \frac{\pm\sqrt{15}}{5}$$
Solution:
a) $$x = \frac{5 \pm \sqrt{3}}{2}$$
Solution:
a) $$p = -5$$