Solving Quadratics by Factoring and Graphing

What are the x-intercepts of a quadratic function also known as?

• Derivatives

• Coefficients

• Zeros, roots, or solutions

• Pivots

How many solutions can a quadratic equation have?

• Only one solution

• Up to two solutions

• Always two solutions

• None of the above

What method is suggested to use when all other methods fail to solve a quadratic?

• Graphing

• Factoring

• Completing the square

• Quadratic formula

What does the zero-product property imply?

• A product can never be zero

• If a product is zero, both factors must be zero

• Zero is not a valid product of real numbers

• If a product is zero, at least one of the factors must be zero

What is the significance of the zero-product property in solving quadratics?

• It helps identify the maximum or minimum point

• It is used to determine the symmetry of the graph

• It allows for the determination of the equation's roots

• It calculates the discriminant

How do you solve a quadratic equation that is already in factored form?

• By applying the quadratic formula

• By completing the square

• By graphing the equation

• By setting each factor equal to zero and solving

What is the first step in solving a quadratic equation by factoring?

• Ensure the equation is set to equal zero

• Draw the graph of the quadratic function

• Identify the a, b, and c values

• Apply the zero-product property

What does setting a factor equal to zero and solving help identify?

• The y-intercept of the quadratic function

• The x-intercepts or solutions of the quadratic equation

• The maximum value of the quadratic function

• The vertex of the parabola

What must you do first when solving a quadratic equation not in factored form?

• Apply the quadratic formula

• Graph the equation

• Find the derivative

• Set the equation equal to zero and factor it

What are the solutions of the quadratic equation x^2 + 10x + 24 = 0?

• x = 6 and x = 4

• x = -6 and x = -4

• x = -6 and x = 4

• x = 6 and x = -4