Forms of Quadratics

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is f(x) = a(x - r1)(x - r2), where r1 and r2 are the roots of the equation.

Front

How do you find the roots of a quadratic equation in factored form?

Back

To find the roots, set each factor equal to zero and solve for x.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Front

How do you determine the vertex from the vertex form of a quadratic?

Back

The vertex is given directly by the values of h and k in the vertex form f(x) = a(x - h)^2 + k.

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 equation x = -b/(2a) in standard form.

Front

How do you find the axis of symmetry from the standard form of a quadratic?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the standard form f(x) = ax^2 + bx + c.

Front

What is the significance of the coefficient 'a' in a quadratic equation?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What are the characteristics of the roots of a quadratic equation?

Back

The roots can be real and distinct, real and equal, or complex, depending on the discriminant (b^2 - 4ac).

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b^2 - 4ac that determines the nature of the roots of the quadratic equation.