Solving Quadratics Review

What is the first step in factoring a quadratic expression?

• Find the discriminant

• Simplify the expression

• Check for the greatest common factor (GCF)

• Expand the expression

Solve the following quadratic equation by factoring: x^2 + 5x + 6 = 0

• x = 0, 6

• x = 2, 3

• x = -2, -3

• x = -6, -1

What is the purpose of completing the square in solving quadratics?

• To simplify the quadratic equation.

• To convert the quadratic equation into a perfect square trinomial.

• To find the x-intercepts of the quadratic equation.

• To determine the vertex of the parabola.

Solve the following quadratic equation by completing the square: x^2 - 6x + 9 = 0

• x = -3

• x = 9

• x = 3

• x = 6

What is the quadratic formula?

• x = (-b ± √(b^2 - ac)) / (2a)

• x = (-b ± √(b^2 - 4ac)) / (2a)

• x = (-b ± √(b^2 + 4ac)) / (a)

• x = (-b ± √(b^2 + 4ac)) / (2a)

Solve the following quadratic equation using the quadratic formula: 2x^2 + 3x - 2 = 0

• The solutions to the quadratic equation 2x^2 + 3x - 2 = 0 are x = 1/2 and x = 2

• The solutions to the quadratic equation 2x^2 + 3x - 2 = 0 are x = 1/2 and x = -2.

• The solutions to the quadratic equation 2x^2 + 3x - 2 = 0 are x = 1 and x = -2

• The solutions to the quadratic equation 2x^2 + 3x - 2 = 0 are x = 2 and x = -1

What is the discriminant of a quadratic equation?

• The discriminant of a quadratic equation is the square root of the expression b^2 - 4ac.

• The discriminant of a quadratic equation is always equal to zero.

• The discriminant of a quadratic equation is the product of the coefficients a, b, and c.

• The discriminant of a quadratic equation is the sum of the coefficients a, b, and c.

Find the discriminant of the quadratic equation: 4x^2 - 5x + 1 = 0

• 1

• 9

• 0

• -9

What are some real-life applications of quadratics?

• Biology, chemistry, geology, sociology

• Literature, history, philosophy, art

• Physics, engineering, computer graphics, economics

• Mathematics, statistics, logic, programming

A ball is thrown into the air with an initial velocity of 20 m/s. The height of the ball can be modeled by the quadratic equation h = -5t^2 + 20t + 10, where h is the height in meters and t is the time in seconds. How long does it take for the ball to reach its maximum height?

• 2

• 4

• 3

• 1