Quadratic Functions - Vertex Form Flashcards

Questions and Answers

What is the standard form of quadratic functions?

k = (4ac - b²) / 4a

y = ax² + bx + c (correct)

h = -b / 2a

y = a(x - h)² + k

What is the vertex form of a quadratic function?

y = ax² + bx + c

x = h

y = a(x - h)² + k (correct)

h = -b / 2a

What formula is used to find h in vertex form?

h = -b / 2a

What formula is used to find k in vertex form?

k = (4ac - b²) / 4a Signup and view all the answers

What coordinates represent the vertex?

(h, k) Signup and view all the answers

What is the axis of symmetry in a quadratic function?

x = h Signup and view all the answers

A quadratic function faces upward when a < 0.

False Signup and view all the answers

A quadratic function faces downward when a < 0.

True Signup and view all the answers

The vertex is a minimum point when a < 0.

False Signup and view all the answers

The vertex is a maximum point when a > 0.

False Signup and view all the answers

Study Notes

Quadratic Functions - Standard Form

The standard form of a quadratic function is expressed as ( y = ax^2 + bx + c ).

Quadratic Function - Vertex Form

Vertex form is defined by the equation ( y = a(x - h)^2 + k ), where ( (h, k) ) is the vertex of the parabola.

Vertex Form - Formula for h

The value of ( h ) can be calculated using the formula ( h = \frac{-b}{2a} ).

Vertex Form - Formula for k

The value of ( k ) is determined by the formula ( k = \frac{4ac - b^2}{4a} ).

Vertex

The vertex of a quadratic function is represented by the point ( (h, k) ), indicating the maximum or minimum of the parabola.

Axis of Symmetry

The axis of symmetry for a quadratic function is given by the vertical line ( x = h ).

When the Quadratic Function Faces Upward

A parabola opens upwards when the coefficient ( a ) is greater than zero ( ( a > 0 ) ).

When the Quadratic Function Faces Downward

A parabola opens downwards when the coefficient ( a ) is less than zero ( ( a < 0 ) ).

When the Vertex is a Minimum Point

The vertex represents a minimum point of the parabola when ( a ) is positive ( ( a > 0 ) ).

When the Vertex is a Maximum Point

The vertex serves as a maximum point of the parabola when ( a ) is negative ( ( a < 0 ) ).

Description

This quiz features key flashcards on the vertex form of quadratic functions. Each card presents important concepts such as the standard form, vertex coordinates, and formulas related to vertex calculations. Perfect for reinforcing your understanding of quadratic functions in mathematics.