Flashcard - Forms of Quadratic Equations

Front

What is a quadratic equation?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is f(x) = ax² + bx + c.

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 upwards or downwards.

Front

How do you find the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function can be found by evaluating the function at x = 0, which gives the point (0, f(0)).

Front

What does it mean for a parabola to have a minimum?

Back

A parabola has a minimum if it opens upwards, meaning the vertex is the lowest point on the graph.

Front

What does it mean for a parabola to have a maximum?

Back

A parabola has a maximum if it opens downwards, meaning the vertex is the highest point on the graph.

Front

How can you determine the zeros of a quadratic function?

Back

The zeros of a quadratic function can be found by setting the function equal to zero and solving for x, either by factoring, using the quadratic formula, or completing the square.

Front

What is the quadratic formula?

Back

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

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry of a parabola is a vertical line that passes through the vertex, dividing the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a).

Front

What are the characteristics of the graph of a quadratic function?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards, has a vertex, an axis of symmetry, and may intersect the x-axis at zero, one, or two points.