Solving Quadratic Equations by Factoring

This lesson covers solving quadratic equations by factoring, using the zero product property, and graphing quadratic functions. It includes examples of solving equations, finding x-intercepts, and determining the vertex of a parabola. The lesson also demonstrates how to write the factored form of a quadratic function from a graph.

What is the zero product property in the context of quadratic equations?

• If a product of two numbers is zero, at least one of the numbers must be zero.

• The product of two numbers is always zero.

• The sum of two numbers is zero.

• None of the above.

How can you solve the equation (x - 9)(5x + 2) = 0 using factoring?

• Multiply the factors and set the equation to zero.

• None of the above.

• Add the factors together and solve for x.

• Set x - 9 = 0 and 5x + 2 = 0, then solve for x.

What is the solution for x in the equation x^2 + 9x = -20 after converting it to standard form?

• x = -5, x = -4

• x = 5, x = -4

• x = -5, x = 4

• x = 5, x = 4

Which method is used to factor the quadratic equation x^2 + 9x + 20 = 0?

• None of the above

• By finding factors of 20 that add up to 9

• By completing the square

• Using the quadratic formula

What are the solutions to the equation 2x^2 - 5x - 3 = 0 after factoring?

• x = -1/2, x = 3

• x = 1/2, x = -3

• x = -3, x = 1/2

• x = 3, x = -1/2

How do you find the vertex of a parabola represented by the equation x^2 - 2x - 8?

• Set the equation to zero and solve for x

• Factor the equation and use the solutions

• None of the above

• Use the formula -b/2a

What are the x-intercepts of the quadratic function f(x) = x^2 - 2x - 8?

• x = -2, x = 4

• x = 4, x = -2

• x = -4, x = 2

• x = 2, x = -4

How can you write the factored form of a quadratic function from its graph?

• Use the x-intercepts to form factors (x - p)(x - q)

• Add the x-intercepts together

• None of the above

• Multiply the x-intercepts together

What is the factored form of the quadratic function if the x-intercepts are -5 and 1?

• f(x) = (x - 5)(x + 1)

• f(x) = (x - 5)(x - 1)

• f(x) = (x + 5)(x + 1)

• f(x) = (x + 5)(x - 1)

What is the vertex of the quadratic function f(x) = (x + 5)(x - 1) if a = 1?

• (-2, 9)

• (2, 9)

• (-2, -9)

• (2, -9)