Solve Quadratics by Factoring (a=1)

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean to factor a quadratic equation?

Back

Factoring a quadratic equation means rewriting it as a product of two binomials, such as (x + p)(x + q) = 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What is the factored form of x² + 6x + 9?

Back

(x + 3)(x + 3) or (x + 3)².

Front

How do you find the solutions of a factored quadratic equation?

Back

Set each factor equal to zero and solve for x.

Front

What are the solutions of the equation (x + 4)(x - 3) = 0?

Back

x = -4 and x = 3.

Front

What is the zero-product property?

Back

If the product of two factors is zero, then at least one of the factors must be zero.

Front

What is the vertex of a parabola represented by a quadratic equation?

Back

The vertex is the highest or lowest point of the parabola, depending on the direction it opens.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

What is the discriminant in a quadratic equation?

Back

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