Graphs of Quadratic Functions Review

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers, as quadratic functions can take any real value for x.

Front

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

Back

The range of a quadratic function that opens upwards is all real numbers greater than or equal to the y-coordinate of the vertex.

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 x-intercepts of a quadratic function?

Back

To find the x-intercepts, set the quadratic function equal to zero 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, given by the formula x = -b/(2a) for a quadratic in the form ax^2 + bx + c.

Front

What does it mean for a quadratic function to open upwards?

Back

A quadratic function opens upwards if the coefficient of the x^2 term (a) is positive, indicating that the vertex is the minimum point.

Front

What does it mean for a quadratic function to open downwards?

Back

A quadratic function opens downwards if the coefficient of the x^2 term (a) is negative, indicating that the vertex is the maximum point.

Front

How can you determine 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.

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.

Front

What is the factored form of a quadratic function?

Back

The factored form of a quadratic function is f(x) = a(x - r1)(x - r2), where r1 and r2 are the roots or x-intercepts.