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Graphing Quadratic Equations quiz

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  • What is the general shape of the graph of any quadratic equation?
    The graph of any quadratic equation is a parabola.
  • How does the sign of the 'a' coefficient in y = ax^2 + bx + c affect the direction the parabola opens?
    If 'a' is positive, the parabola opens upward; if 'a' is negative, it opens downward.
  • What is the vertex of a parabola in the equation y = a(x-h)^2 + k?
    The vertex is at the point (h, k).
  • How do you determine the axis of symmetry for a parabola in vertex form?
    The axis of symmetry is the vertical line x = h.
  • What effect does the value of 'a' have on the width of the parabola?
    If |a| > 1, the parabola is narrower; if 0 < |a| < 1, it is wider.
  • How does adding or subtracting a value inside the squared term (x-h)^2 affect the graph?
    It shifts the graph horizontally: subtracting h shifts right, adding h shifts left.
  • How does adding or subtracting a value outside the squared term affect the graph?
    It shifts the graph vertically: adding k shifts up, subtracting k shifts down.
  • What is the domain of any quadratic function?
    The domain is all real numbers.
  • How do you find the x-intercepts of a quadratic equation in standard form?
    Set y = 0 and solve using the quadratic formula.
  • What does the discriminant (b^2 - 4ac) tell you about the graph of a quadratic?
    It tells how many real x-intercepts the graph has: two if positive, one if zero, none if negative.
  • How do you find the y-intercept of a quadratic equation?
    Plug x = 0 into the equation and solve for y.
  • What is the formula for the axis of symmetry in standard form y = ax^2 + bx + c?
    The axis of symmetry is x = -b/(2a).
  • How do you find the vertex of a quadratic in standard form?
    The x-value is -b/(2a); plug this into the equation to find the y-value.
  • What happens to the graph of y = ax^2 + bx + c if 'a' is a fraction between -1 and 1?
    The parabola becomes wider due to vertical compression.
  • Why is the form y = a(x-h)^2 + k called 'vertex form'?
    Because the vertex is easily identified as (h, k) and the form makes graphing straightforward.