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 does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of 'a'.

Tags

CCSS.HSF-IF.C.7A

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 whether it opens upwards or downwards.

Front

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

Back

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

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 equation x = h, where h is the x-coordinate of the vertex.

Front

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

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at x = 0 (y = c in standard form).

Tags

CCSS.HSF-IF.C.7A

Front

How do you convert a quadratic function from standard form to vertex form?

Back

To convert to vertex form, use the method of completing the square: y = a(x - h)² + k.

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.