Transformations of Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form y = 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 y = 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

How does the value of 'a' affect the graph of a quadratic function?

Back

The value of 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width (narrower if |a| > 1, wider if |a| < 1).

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 formula x = -b/(2a).

Front

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

Back

The 'c' value represents the y-intercept of the quadratic function, which is the point where the graph intersects the y-axis.

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you convert from standard form to vertex form?

Back

To convert from standard form to vertex form, you can complete the square.

Front

What is the effect of adding a constant to a quadratic function?

Back

Adding a constant to a quadratic function shifts the graph vertically. For example, y = x² + 3 shifts the graph up by 3 units.

Front

What does it mean for a quadratic function to have real roots?

Back

A quadratic function has real roots if its graph intersects the x-axis, which occurs when the discriminant (b² - 4ac) is greater than or equal to zero.