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Graphing Quadratic Equations quiz

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  • What is the general form of a quadratic equation used for graphing?
    The general form is y = ax^2 + bx + c, where a ≠ 0.
  • What is the name of the U-shaped curve formed when graphing a quadratic equation?
    The curve is called a parabola.
  • How does the sign of the coefficient 'a' affect the direction a parabola opens?
    If 'a' is positive, the parabola opens upward; if 'a' is negative, it opens downward.
  • What is the vertex of a parabola, and what does it represent?
    The vertex is the highest or lowest point on the parabola, depending on whether it opens downward or upward.
  • What is the axis of symmetry for a parabola, and how is it related to the vertex?
    The axis of symmetry is a vertical line that passes through the vertex and divides the parabola evenly.
  • How does adding or subtracting a value inside the squared term, like (x - h)^2, affect the graph?
    It shifts the graph horizontally: right if h is positive, left if h is negative.
  • How does adding or subtracting a value outside the squared term, like x^2 + k, affect the graph?
    It shifts the graph vertically: up if k is positive, down if k is negative.
  • What effect does increasing the absolute value of 'a' have on the width of the parabola?
    A larger |a| makes the parabola narrower, while a smaller |a| (between 0 and 1) makes it wider.
  • What is the vertex form of a quadratic equation?
    The vertex form is y = a(x - h)^2 + k.
  • How can you quickly find the vertex from a quadratic in vertex form?
    The vertex is at the point (h, k).
  • How do you find the axis of symmetry from a quadratic in vertex form?
    The axis of symmetry is the vertical line x = h.
  • How do you find the x-intercepts of a quadratic equation?
    Set y = 0 and solve the equation for x, often using factoring or the quadratic formula.
  • What does the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / (2a) give you when graphing?
    It gives the x-intercepts (roots) of the parabola.
  • What does the value -b/(2a) represent in the context of graphing quadratics?
    It represents the x-coordinate of the vertex and the axis of symmetry.
  • How do you find the y-intercept of a quadratic equation in standard form?
    Plug in x = 0 and solve for y; the result is the y-intercept.