Quadratic Equations and Graphing
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Questions and Answers

What is the general form of a quadratic equation?

  • ax + bx + c = 0
  • ax^2 + bx + c = 0 (correct)
  • ax^4 + bx^3 + cx^2 = 0
  • ax^3 + bx^2 + cx = 0
  • The graph of a quadratic equation is a straight line.

    False

    What is the formula for the surface area of a rectangular prism?

    2(lw + lh + wh)

    The formula for the volume of a cylinder is _______________.

    <p>πr^2h</p> Signup and view all the answers

    Match the following features of a quadratic equation graph with their descriptions:

    <p>Vertex = The highest or lowest point of the parabola. Axis of symmetry = The vertical line that passes through the vertex. x-intercepts = The points where the graph crosses the x-axis. y-intercept = The point where the graph crosses the y-axis.</p> Signup and view all the answers

    What is the conversion between units for volume?

    <p>1 cubic centimeter (cm³) = 1 milliliter (mL)</p> Signup and view all the answers

    Study Notes

    Quadratic Equations

    • Definition: A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable (usually x) is two.
    • General form: ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0.
    • Factoring: Some quadratic equations can be solved by factoring into the product of two binomials.
    • Quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a, used when factoring is not possible.

    Graphing

    • Cartesian plane: A two-dimensional coordinate system with x-axis and y-axis.
    • Graph of a quadratic equation: A parabola that opens upward or downward.
    • Key features:
      • Vertex: The lowest or highest point of the parabola.
      • Axis of symmetry: The vertical line that passes through the vertex.
      • x-intercepts: The points where the graph crosses the x-axis.
      • y-intercept: The point where the graph crosses the y-axis.

    Surface Area and Volume

    Surface Area

    • Formula for surface area of a rectangular prism: 2(lw + lh + wh), where l is length, w is width, and h is height.
    • Formula for surface area of a cylinder: 2πr(h + r), where r is radius and h is height.

    Volume

    • Formula for volume of a rectangular prism: lwh, where l is length, w is width, and h is height.
    • Formula for volume of a cylinder: πr^2h, where r is radius and h is height.
    • Conversion between units: 1 cubic centimeter (cm³) = 1 milliliter (mL)

    Quadratic Equations

    • A quadratic equation is a polynomial equation with a degree of two, where the highest power of the variable (usually x) is two.
    • The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0.
    • Some quadratic equations can be solved by factoring into the product of two binomials.
    • The quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a, used when factoring is not possible.

    Graphing

    • The Cartesian plane is a two-dimensional coordinate system with x-axis and y-axis.
    • The graph of a quadratic equation is a parabola that opens upward or downward.
    • The key features of a parabola include:
      • The vertex, which is the lowest or highest point of the parabola.
      • The axis of symmetry, which is the vertical line that passes through the vertex.
      • The x-intercepts, which are the points where the graph crosses the x-axis.
      • The y-intercept, which is the point where the graph crosses the y-axis.

    Surface Area and Volume

    Surface Area

    • The formula for the surface area of a rectangular prism is 2(lw + lh + wh), where l is length, w is width, and h is height.
    • The formula for the surface area of a cylinder is 2πr(h + r), where r is radius and h is height.

    Volume

    • The formula for the volume of a rectangular prism is lwh, where l is length, w is width, and h is height.
    • The formula for the volume of a cylinder is πr^2h, where r is radius and h is height.
    • 1 cubic centimeter (cm³) is equal to 1 milliliter (mL).

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    Description

    This quiz covers quadratic equations, including definition, general form, factoring, and quadratic formula, as well as graphing on the Cartesian plane.

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