Quadratic Formula

Front

What is the standard form of a quadratic equation?

Back

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

Front

What does the quadratic formula state?

Back

The quadratic formula states that the solutions for the quadratic equation ax² + bx + c = 0 can be found using x = (-b ± √(b² - 4ac)) / (2a).

Front

How do you identify the coefficients a, b, and c in a quadratic equation?

Back

In the quadratic equation ax² + bx + c = 0, 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term.

Front

What is the discriminant in the context of the quadratic formula?

Back

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

Front

What does a positive discriminant indicate about the roots of a quadratic equation?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Front

What does a zero discriminant indicate about the roots of a quadratic equation?

Back

A zero discriminant indicates that the quadratic equation has exactly one real root (a repeated root).

Front

What does a negative discriminant indicate about the roots of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has no real roots, but two complex roots.

Front

How can you convert a quadratic equation from standard form to vertex form?

Back

To convert a quadratic equation from standard form (ax² + bx + c) to vertex form (a(x-h)² + k), you can complete the square.

Front

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

Back

The vertex of a parabola is the point (h, k) in the vertex form of the equation a(x-h)² + k, where h = -b/(2a) and k is the value of the function at x = h.

Front

What is the axis of symmetry in a quadratic function?

Back

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