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.

Tags

CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSG.GPE.B.6

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).