Factoring Quadratics

Front

What are the x-intercepts of a quadratic equation?

Back

The x-intercepts are the points where the graph of the quadratic equation crosses the x-axis, represented as the values of x when y=0.

Front

How do you factor the expression 2c^2 + 2c - 84?

Back

First, take out the greatest common factor (GCF), which is 2. The factored form is 2(c+7)(c-6).

Front

What do the 'Zeros' represent on a quadratic equation graph?

Back

The 'Zeros' represent the x-intercepts of the graph, which are the values of x that make the quadratic equation equal to zero.

Front

Solve the equation 3x^2 - 30 = -9x by factoring.

Back

Rearranging gives 3x^2 + 9x - 30 = 0. Factoring gives (x+5)(3x-6)=0, so x=2 and x=-5.

Front

Solve by factoring: x^2 + 15x + 44 = 0.

Back

The factored form is (x+11)(x+4)=0, so the solutions are x=-11 and x=-4.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of the quadratic function, depending on the direction of the parabola.

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 quadratic formula?

Back

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

Front

What does the discriminant tell us about a quadratic equation?

Back

The discriminant (b^2 - 4ac) indicates the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.