Quadratic Functions - Axis of Symmetry 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 and a ≠ 0.

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 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. It can be found using the formula x = -b/(2a).

Front

How do you find the vertex of a quadratic function?

Back

The vertex can be found using the formula (h, k), where h = -b/(2a) and k = f(h).

Front

What does the vertex represent in a quadratic function?

Back

The vertex represents the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

Front

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

Back

The 'a' value determines the direction of the parabola: if a > 0, it opens upwards (min), and if a < 0, it opens downwards (max).

Front

How do you determine if a quadratic function has a maximum or minimum value?

Back

If the parabola opens upwards (a > 0), it has a minimum value. If it opens downwards (a < 0), it has a maximum value.

Front

What are x-intercepts in a quadratic function?

Back

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

Front

How do you find the x-intercepts of a quadratic function?

Back

The x-intercepts can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (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).