Quadratic Transformation Review

Front

What is the axis of symmetry of a parabola?

Back

The axis of symmetry of a parabola is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a) for a quadratic equation in the form y = ax^2 + bx + c.

Front

How do you reflect a parabola across the x-axis?

Back

To reflect a parabola across the x-axis, you multiply the entire function by -1. For example, the reflection of y = x^2 is y = -x^2.

Front

What does it mean to compress a parabola vertically by a factor of 1/2?

Back

Compressing a parabola vertically by a factor of 1/2 means that the y-values of the function are halved, making the parabola wider. For example, y = (1/2)x^2 is a vertical compression of y = x^2.

Front

What is the effect of shifting a parabola 4 units to the right?

Back

Shifting a parabola 4 units to the right involves replacing x with (x - 4) in the function. For example, the function y = x^2 becomes y = (x - 4)^2.

Front

How do you find the vertex of a parabola given in standard form?

Back

To find the vertex of a parabola in standard form y = ax^2 + bx + c, use the formula for the x-coordinate: x = -b/(2a). Then substitute this x-value back into the equation to find the y-coordinate.

Front

What is the vertex of the parabola y = 2x^2 + 8x - 6?

Back

The vertex of the parabola y = 2x^2 + 8x - 6 is (-2, -14). This can be found using the vertex formula.

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers, as quadratic functions are defined for every value of x.

Front

What does it mean to shift a parabola 1 unit up?

Back

Shifting a parabola 1 unit up involves adding 1 to the entire function. For example, y = x^2 becomes y = x^2 + 1.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How do you determine if a parabola opens upwards or downwards?

Back

A parabola opens upwards if the coefficient 'a' in the quadratic equation y = ax^2 + bx + c is positive. It opens downwards if 'a' is negative.