Quadratic Equations

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form of ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does the graph of a quadratic equation look like?

Back

The graph of a quadratic equation is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Front

What determines if a parabola opens upwards or downwards?

Back

A parabola opens upwards if the coefficient 'a' in the quadratic equation ax² + bx + c is positive, and it opens downwards if 'a' is negative.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens downwards or upwards.

Front

How do you find the vertex of a quadratic equation in standard form?

Back

The vertex (h, k) can be found using the formula h = -b/(2a) and k = f(h), where f(x) is the quadratic function.

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = h, where h is the x-coordinate of the vertex.

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum value occurs at the vertex if the parabola opens downwards, and the minimum value occurs at the vertex if it opens upwards.

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is expressed as y = a(x - r1)(x - r2), where r1 and r2 are the roots or solutions of the equation.

Front

How do you find the roots of a quadratic equation?

Back

The roots can be found using factoring, completing the square, or applying the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation.