Characteristics of Quadratic Functions

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 and a ≠ 0.

Front

What is the vertex of a quadratic function?

Back

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

Front

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

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the point (0, f(0)).

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 are x-intercepts?

Back

X-intercepts are the points where the graph of the function crosses the x-axis, found by solving the equation f(x) = 0.

Front

What does it mean if a quadratic function has no real x-intercepts?

Back

If a quadratic function has no real x-intercepts, it means the graph does not cross the x-axis, indicating that the discriminant (b² - 4ac) is less than zero.

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 form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex.

Front

How can you determine if the vertex is a maximum or minimum?

Back

If a > 0, the vertex is a minimum; if a < 0, the vertex is a maximum.

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

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