Characteristics and Transformations of Quadratic Graphs

Front

What is a parabola?

Back

A parabola is a symmetrical, curved shape that represents the graph of a quadratic function. It can open upwards or downwards.

Front

What is the vertex of a parabola?

Back

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

Front

What is the axis of symmetry in a parabola?

Back

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

Front

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

Back

To find the y-intercept, set x = 0 in the quadratic equation and solve for y.

Front

What does the term 'transformation' mean in the context of quadratic functions?

Back

Transformation refers to changes made to the graph of a function, such as shifting, reflecting, or stretching.

Front

What is the effect of a negative sign in front of a quadratic function?

Back

A negative sign reflects the parabola across the x-axis.

Front

How does shifting a parabola to the left affect its equation?

Back

Shifting a parabola to the left by 'h' units changes the equation to y = (x + h)² + k.

Front

How does shifting a parabola down affect its equation?

Back

Shifting a parabola down by 'k' units changes the equation to y = x² - k.

Front

What is the standard form of a quadratic function?

Back

The standard form is y = ax² + 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 its width.