Quadratic Transformations

Front

What is the vertex form of a quadratic function?

Back

f(x) = a(x-h)² + k

Front

What does the vertex of a parabola represent?

Back

The vertex represents the maximum or minimum point of the parabola.

Front

What is the significance of the 'a' value in the vertex form?

Back

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

Front

How do you find the x-intercepts of a quadratic function?

Back

Set f(x) = 0 and solve for x.

Front

What is the axis of symmetry in a parabola?

Back

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

Front

What is the standard form of a quadratic function?

Back

f(x) = ax² + bx + c

Front

How do you convert from standard form to vertex form?

Back

Use the method of completing the square.

Front

What is the formula for the vertex of a parabola in standard form?

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h).

Front

What does it mean if a quadratic function has no real x-intercepts?

Back

It means the parabola does not cross the x-axis, indicating that the discriminant (b² - 4ac) is less than zero.

Front

How do you solve a quadratic equation by taking the square root?

Back

Isolate the x² term and then take the square root of both sides.