0.50 - Domain and Range of Quadratics

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) for which the function is defined. For most quadratic functions, the domain is all real numbers, denoted as R.

Front

How do you find the domain of a quadratic function modeled by h(t) = -4.9t^2 + 14.7t + 3.5?

Back

To find the domain, identify the time interval during which the height is non-negative. For h(t), the domain is D:{0<=t<=3.2}.

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. It is determined by the vertex of the parabola and the direction it opens.

Front

How do you find the range of the function y = -2x^2 + 9x - 1?

Back

To find the range, determine the vertex of the parabola. The maximum value occurs at the vertex, which is y <= 9.1.

Front

What is the vertex of a quadratic function?

Back

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

Front

How do you find the vertex of the function y = x^2 - 5x + 2?

Back

The vertex can be found using the formula x = -b/(2a). For this function, the vertex is at (2.5, -4.3).

Front

What does it mean if a quadratic function opens upwards?

Back

If a quadratic function opens upwards, it means the coefficient of the x^2 term is positive, and the vertex represents the minimum point of the function.

Front

What does it mean if a quadratic function opens downwards?

Back

If a quadratic function opens downwards, it means the coefficient of the x^2 term is negative, and the vertex represents the maximum point of the function.

Front

How do you determine the maximum height of an object launched from a height?

Back

The maximum height can be found by evaluating the quadratic function at the vertex, which gives the highest point the object reaches.

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, representing the output value when the input (x) is zero.