AAC #1 Factoring and Solving Quadratics

Front

What are the solutions, roots, x-intercepts, and zeros of a quadratic equation?

Back

They are all the same thing; they refer to the values of x where the quadratic equation equals zero.

Front

How do you rearrange and factor the equation b² = -35 + 12b?

Back

Rearranging gives b² - 12b + 35 = 0, which factors to (b - 5)(b - 7) = 0, giving solutions b = 5 and b = 7.

Front

Factor the expression 4x² - 81.

Back

The expression factors to (2x - 9)(2x + 9).

Front

Factor the quadratic k² - 2k - 24.

Back

The expression factors to (k - 6)(k + 4).

Front

How do you find the zeros of the equation (x + 10)(x - 2) = 0?

Back

Set each factor to zero: x + 10 = 0 gives x = -10, and x - 2 = 0 gives x = 2.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants.

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 does it mean for a quadratic to be factored?

Back

Factoring a quadratic means expressing it as a product of its linear factors.

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

What is the axis of symmetry in a quadratic function?

Back

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