Vertex and Parent Function

Front

What is the definition of a vertex in a graph?

Back

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

Front

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

Back

The vertex of a quadratic function in standard form, y = ax^2 + bx + c, can be found using the formula: x = -b/(2a). The y-coordinate can be found by substituting this x value back into the function.

Front

What is the vertex of the parent function y = x^2?

Back

The vertex of the parent function y = x^2 is (0, 0).

Front

How does the vertex of a graph affect its shape?

Back

The vertex determines the direction of the graph's opening (upward or downward) and the location of the maximum or minimum point.

Front

What is the significance of the vertex in application-based problems?

Back

The vertex often represents optimal solutions in real-world problems, such as maximum profit or minimum cost.

Front

What is the vertex of the function y = (x - 2)^2 + 3?

Back

The vertex of the function y = (x - 2)^2 + 3 is (2, 3).

Front

How can transformations affect the vertex of a function?

Back

Transformations such as translations, reflections, and stretches/compressions can change the position of the vertex in the coordinate plane.

Front

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

Back

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

Front

How do you find the vertex of a parabola given its graph?

Back

To find the vertex of a parabola from its graph, identify the highest or lowest point on the curve, which is the vertex.

Front

What is the vertex of the function y = -x^2 + 4?

Back

The vertex of the function y = -x^2 + 4 is (0, 4).