Algebra Chapter 4 Quiz Flashcards

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Questions and Answers

What is a quadratic function?

  • An equation with x
  • An equation with x^4
  • An equation with x^3
  • An equation with x^2 (correct)

What is the general form of a quadratic function?

ax^2 + bx + c

What shape does the graph of a quadratic function take?

U-shaped

What is vertex form of a quadratic function?

<p>y = a(x - h)^2 + k</p> Signup and view all the answers

What is the minimum value of a quadratic function?

<p>lowest y-value</p> Signup and view all the answers

What is the maximum value of a quadratic function?

<p>highest y-value</p> Signup and view all the answers

What is the standard form of a quadratic function?

<p>y = ax^2 + bx + c</p> Signup and view all the answers

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Study Notes

Quadratic Functions

  • Defined as an equation that includes ( x^2 ), expressed in the form ( ax^2 + bx + c ) or vertex form ( a(x-h)^2 + k ).
  • Quadratic functions characterize a wide range of real-world phenomena, including projectile motion and profit maximization.

Parabolas

  • The graph representation of a quadratic function is called a parabola, which has a distinct "U" shape.
  • Parabolas can open upwards (minimum value) or downwards (maximum value), depending on the sign of the coefficient ( a ).

Vertex Form

  • The vertex form of a quadratic function is given by ( y = a(x-h)^2 + k ).
  • Here, ( (h, k) ) represents the vertex of the parabola, which is the highest or lowest point based on the direction the parabola opens.

Minimum Value

  • The minimum value refers to the lowest point on the graph of a parabola that opens upwards.
  • Occurs at the vertex, making it crucial in applications that seek to find optimal solutions.

Maximum Value

  • The maximum value is the highest point on the graph of a parabola that opens downwards.
  • It also exists at the vertex and is significant in scenarios that require maximizing a quantity.

Standard Form

  • Standard form of a quadratic function is represented as ( y = ax^2 + bx + c ).
  • This form is useful for determining the y-intercept (value of ( c )) and extracting coefficients that inform about the parabola's shape and position.

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