Quadratic Equations Quiz

What are the solutions to a quadratic equation?

• Two distinct real solutions

• One real solution

• Two complex solutions

• All of the above

Why does the equation have to be set to 0 when solving?

• To simplify the equation and isolate the variable

• To ensure the equation remains balanced

• To allow the use of factoring and zero-product property

• No specific reason; it is a standard convention

Solve by factoring: (3x^2 - 11x = 4)

• x = 4, x = -1/3

• x = 4, x = 1/3

• x = -4, x = 1/3

• x = -4, x = -1/3

Solve by finding square roots: (49x^2 - 196 = 0)

• x = 2

• x = -2

• x = 2 or x = -2

• x = 0

Solve by graphing. Show your work to get credit: (y = (x - 5)^2 - 4)

Solve by completing the square. Write your answers in simplest radical form: (x^2 + 14x + 5 = 0)

Rewrite the equation in vertex form: (y = x^2 + 4x + 1)

• y = (x + 2)^2 - 3

• y = (x - 2)^2 + 3

• y = (x + 2)^2 + 3

• y = (x - 2)^2 - 3

Solve using the Quadratic Formula. Write your answers in simplest radical form: 2x(x - 3) = 6.

Use the discriminant to determine the number of REAL solutions for the equation 4x^2 + 144 = -48x.

Write the quotient as a complex number: (4-3i)/(5+i).