Characteristics and Transformations of Quadratics

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

Identify the x-intercepts of a quadratic function.

Back

The x-intercepts are the points where the graph intersects the x-axis, found by setting the quadratic equation to zero.

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, passing through the vertex.

Front

Define a parabola.

Back

A parabola is the U-shaped graph of a quadratic function, which can open upwards or downwards.

Front

What does it mean for a quadratic function to be in standard form?

Back

A quadratic function is in standard form when it is expressed as f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

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

Back

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

Front

How do you find the y-intercept of a quadratic function?

Back

The y-intercept is found by evaluating the function at x = 0, which gives the point (0, c) in standard form.

Front

What is the formula for finding the vertex of a quadratic function in standard form?

Back

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

Front

What are the roots of a quadratic equation?

Back

The roots are the values of x that make the quadratic equation equal to zero, also known as the solutions or x-intercepts.

Front

Explain the concept of completing the square.

Back

Completing the square is a method used to convert a quadratic equation into vertex form by rewriting it as (x - p)^2 = q.