Quadratics

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 vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function.

Front

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation.

Front

What is the y-intercept of a quadratic function?

Back

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

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 range of a quadratic function that opens downwards?

Back

The range is all real numbers less than or equal to the y-coordinate of the vertex.

Front

What is the effect of changing the 'h' value in the vertex form of a quadratic function?

Back

Changing the 'h' value in the vertex form f(x) = a(x - h)² + k translates the graph horizontally.

Front

What is the effect of changing the 'k' value in the vertex form of a quadratic function?

Back

Changing the 'k' value in the vertex form f(x) = a(x - h)² + k translates the graph vertically.

Front

How do you determine the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex, which can be found using the vertex formula.