Quadratic Functions Root and Vertex

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c.

Front

What is the vertex of a parabola?

Back

The vertex of a parabola 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 a quadratic function in standard form?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))).

Front

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

Back

The 'a' value determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

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 equation x = -b/(2a).

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating f(0).

Front

How can you determine the number of solutions a quadratic equation has?

Back

The number of solutions can be determined using the discriminant (b² - 4ac): if > 0, two solutions; = 0, one solution; < 0, no solutions.

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex; it is the y-coordinate of the vertex.

Front

What does it mean if a parabola opens upwards?

Back

If a parabola opens upwards, it has a minimum vertex and the function's values increase as you move away from the vertex.