Quadratic Transformations

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 parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on the direction it opens.

Front

What does the axis of symmetry represent in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, passing through the vertex.

Front

How do you find the vertex from the standard form of a quadratic function?

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, and then substituting it back into the function to find the y-coordinate.

Front

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

Back

Changing the value of 'a' affects the width and direction of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

Front

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

Back

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

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 a transformation in the context of quadratic functions?

Back

A transformation refers to changes made to the parent function, such as shifts, stretches, or reflections.

Front

What does a horizontal shift to the left mean in a quadratic function?

Back

A horizontal shift to the left means the graph of the function moves leftward by a certain number of units, represented by f(x + h) where h > 0.