Vertex and Parent Function II

Front

What is a vertex in the context of a graph?

Back

The vertex is the point where the graph changes direction, often representing the minimum or maximum point of a function.

Front

What is a parent function?

Back

A parent function is the simplest form of a function in a family of functions, which retains the essential characteristics of that family.

Front

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

Back

For a quadratic function in standard form y = ax^2 + bx + c, the vertex can be found using the formula x = -b/(2a) and then substituting x back into the function to find y.

Front

What is the general shape of a quadratic function's graph?

Back

The graph of a quadratic function is a parabola, which opens upwards if the leading coefficient is positive and downwards if it is negative.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum value of the function, depending on the direction the parabola opens.

Front

How can transformations affect the vertex of a parent function?

Back

Transformations such as translations, reflections, and stretches/compressions can change the position of the vertex of a parent function.

Front

What is the effect of a vertical stretch on the graph of a function?

Back

A vertical stretch makes the graph narrower, increasing the distance between points on the graph and the x-axis.

Front

What is the effect of a vertical compression on the graph of a function?

Back

A vertical compression makes the graph wider, decreasing the distance between points on the graph and the x-axis.

Front

How do you determine if two graphs have the same vertex?

Back

Two graphs have the same vertex if their coordinates (x, y) of the vertex point are identical.

Front

What is the relationship between the vertex and the axis of symmetry in a parabola?

Back

The vertex lies on the axis of symmetry, which is a vertical line that divides the parabola into two mirror-image halves.