Quadratics Domain and Range

Front

What is the range of a quadratic function?

Back

The range of a quadratic function is the set of all possible output values (y-values) that the function can produce. For a parabola that opens upwards, the range is from the vertex's y-value to infinity. For example, if the vertex is at (0, -1), the range is y ≥ -1.

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is the set of all possible input values (x-values) that can be used in the function. For quadratic functions, the domain is usually all real numbers.

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards. It represents the maximum or minimum value of the function.

Front

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

Back

To find the y-intercept of a quadratic function, set x = 0 and solve for y. The y-intercept is the point where the graph crosses the y-axis.

Front

What is an x-intercept?

Back

An x-intercept is a point where the graph of a function crosses the x-axis. To find x-intercepts, set y = 0 and solve 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. It passes through the vertex and can be found using the formula x = -b/(2a) for a quadratic in the form ax^2 + bx + c.

Front

What is the standard form of a quadratic function?

Back

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

Front

What does the coefficient 'a' in a quadratic function indicate?

Back

The coefficient 'a' determines the direction of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the significance of the ordered pair (h, k) in vertex form?

Back

In the vertex form of a quadratic function, f(x) = a(x - h)^2 + k, the ordered pair (h, k) represents the vertex of the parabola.

Front

How can you determine if a quadratic function has a maximum or minimum value?

Back

If the coefficient 'a' is positive, the function has a minimum value at the vertex. If 'a' is negative, the function has a maximum value at the vertex.