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Graphing Quadratic Equations definitions

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  • Quadratic Equation
    An expression in the form y = ax² + bx + c, where a is not zero, creating a U-shaped graph.
  • Parabola
    A smooth, U-shaped curve representing the graph of a quadratic equation.
  • Vertex
    The highest or lowest point on a parabola, indicating its maximum or minimum value.
  • Axis of Symmetry
    A vertical line dividing a parabola into two mirror-image halves, passing through the vertex.
  • Standard Form
    The format y = ax² + bx + c for quadratic equations, useful for applying the quadratic formula.
  • Vertex Form
    The format y = a(x-h)² + k, making it easy to identify the vertex and graph shifts.
  • Coefficient
    A numerical factor multiplying a variable, such as a, b, or c in quadratic equations.
  • Intercept
    A point where the graph crosses the x-axis or y-axis, indicating zero values for one variable.
  • X Intercept
    A point where the parabola crosses the x-axis, found by setting y to zero.
  • Y Intercept
    A point where the parabola crosses the y-axis, found by setting x to zero.
  • Discriminant
    The expression b² - 4ac, determining the number of x intercepts for a quadratic graph.
  • Horizontal Shift
    A movement of the parabola left or right, controlled by the value h in vertex form.
  • Vertical Shift
    A movement of the parabola up or down, controlled by the value k in vertex form.
  • Vertical Stretch
    A transformation making the parabola narrower, caused by a coefficient greater than one.
  • Vertical Compression
    A transformation making the parabola wider, caused by a coefficient between -1 and 1.
  • Direction
    The way the parabola opens, upward for positive a, downward for negative a.
  • Square Root Property
    A method for solving equations involving squared terms, useful for finding intercepts.
  • Quadratic Formula
    An equation providing solutions for ax² + bx + c = 0, revealing x intercepts and symmetry.
  • Symmetry
    A feature where the parabola's left and right sides are mirror images across the axis.
  • Maximum
    The highest value of a parabola, occurring at the vertex when a is negative.
  • Minimum
    The lowest value of a parabola, occurring at the vertex when a is positive.
  • Input Value
    A value substituted for x in the equation to generate corresponding output values.
  • Output Value
    A value produced for y after substituting x into the quadratic equation.
  • Continuous Curve
    A smooth, unbroken line representing the graph of a quadratic equation.
  • Intercept Formula
    A calculation for finding where the graph crosses axes, using substitutions for x or y.
  • Width
    The measure of how wide or narrow a parabola appears, determined by the coefficient a.
  • U Shape
    The characteristic form of a parabola, opening upward or downward.
  • Mirror Image
    The identical appearance of the parabola's sides across the axis of symmetry.
  • Solution
    A value of x that satisfies the quadratic equation, often corresponding to x intercepts.