About The Quadratic Formula:
We previously learned how to solve a quadratic equation using factoring and completing the square. Factoring is simple, but it doesn't always work. Completing the square works for all scenarios, but it is very tedious. The quadratic formula allows us to quickly solve any quadratic equation. With this method, we will write our quadratic equation in standard form. Then we can plug in for a, b, and c in the quadratic formula and simplify.
Test Objectives
- Demonstrate the ability to place a quadratic equation in standard form
- Demonstrate the ability to solve a quadratic equation using the quadratic formula
- Demonstrate the ability to solve a quadratic equation with a complex solution
#1:
Instructions: Solve each equation using the quadratic formula.
a) $$-8m^2 - 8m=-18$$
b) $$3n^2 - 5=0$$
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#2:
Instructions: Solve each equation using the quadratic formula.
a) $$5p^2 - 6p=32$$
b) $$-5n^2=-80$$
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#3:
Instructions: Solve each equation using the quadratic formula.
a) $$2x^2 - 28=-x$$
b) $$8n^2 + 2=-1$$
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#4:
Instructions: Solve each equation using the quadratic formula.
a) $$-10b^2 - b - 17=-10$$
b) $$4a^2 + 10a - 16=-5$$
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#5:
Instructions: Solve each equation using the quadratic formula.
a) $$3x^2 + 8=-7x - 5x^2$$
b) $$5r^2 + 9r=r^2 - 8$$
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Written Solutions:
#1:
Solutions:
a) $$m=\frac{-1 \pm \sqrt{10}}{2}$$
b) $$n= \pm \frac{\sqrt{15}}{3}$$
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#2:
Solutions:
a) $$p=\frac{16}{5}, -2$$
b) $$n= \pm 4$$
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#3:
Solutions:
a) $$x=\frac{7}{2}, -4$$
b) $$n= \pm \frac{\hspace{.25em}i\sqrt{6}}{4}$$
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#4:
Solutions:
a) $$b=\frac{-1 \pm 3i\sqrt{31}}{20}$$
b) $$a=\frac{-5 \pm \sqrt{69}}{4}$$
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#5:
Solutions:
a) $$x=\frac{-7 \pm 3i\sqrt{23}}{16}$$
b) $$r=\frac{-9 \pm i\sqrt{47}}{8}$$
