Quadratic Characteristics!

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form f(x) = ax^2 + 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 written as y = ax^2 + bx + c.

Front

What is the vertex of a quadratic function?

Back

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

Front

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

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the point (0, c) where c is the constant term.

Front

What are x-intercepts?

Back

X-intercepts are the points where the graph of the function crosses the x-axis, found by setting the function equal to zero and solving for x.

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 does the discriminant of a quadratic equation indicate?

Back

The discriminant, given by b^2 - 4ac, indicates the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

What is the range of a quadratic function that opens upwards?

Back

The range is the set of all possible output values (y-values), typically starting from the vertex's y-coordinate to infinity, expressed as [k, ∞) where k is the y-coordinate of the vertex.

Front

What is the increasing interval of a quadratic function that opens upwards?

Back

The increasing interval is the range of x-values where the function is rising, typically from the vertex to positive infinity, expressed as (h, ∞) where h is the x-coordinate of the vertex.

Front

What is the decreasing interval of a quadratic function that opens downwards?

Back

The decreasing interval is the range of x-values where the function is falling, typically from negative infinity to the vertex, expressed as (-∞, h) where h is the x-coordinate of the vertex.