Quadratics Characteristics

Front

What is the range of a quadratic function when the vertex is at the minimum point?

Back

The range is all real numbers greater than or equal to the y-coordinate of the vertex.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on its orientation.

Front

How do you determine the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers unless specified otherwise by a context, such as a physical scenario.

Front

What is the standard form of a quadratic function?

Back

The standard form is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

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

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width.

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

How can you find the maximum height of a projectile modeled by a quadratic function?

Back

The maximum height can be found by evaluating the function at the vertex, which occurs at x = -b/(2a).

Front

What is the effect of changing the 'c' value in the standard form of a quadratic function?

Back

Changing the 'c' value shifts the graph vertically up or down without affecting its shape.

Front

What is the relationship between the roots of a quadratic function and its graph?

Back

The roots (or x-intercepts) are the points where the graph intersects the x-axis, indicating the values of x for which f(x) = 0.

Front

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

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the value of c in the standard form.