Weekly Summative: Factoring and solving x^2+bx+c = 0

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What are the zeros of a quadratic equation?

Back

The zeros of a quadratic equation are the values of x that make the equation equal to zero. They are also known as the roots of the equation.

Front

How do you find the zeros of the quadratic equation x² + 4x + 4 = 0?

Back

Factoring gives (x + 2)(x + 2) = 0, so the zero is x = -2.

Front

What does it mean to solve a quadratic equation by factoring?

Back

Solving by factoring involves rewriting the quadratic equation as a product of two binomials and then setting each factor equal to zero.

Front

What are the roots of the function f(x) = (x - 1)(x + 5)?

Back

The roots are x = 1 and x = -5.

Front

What is another term for the roots of a quadratic equation?

Back

Another term for the roots is 'zeros'.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function.

Front

How do you determine the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the standard form y = ax² + bx + c.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac, which determines the nature of the roots.