Exponential and Logarithmic Functions Quiz
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Questions and Answers

What are the conditions for the quadratic equation $f(x) = abx-h ± k$ to have real roots?

  • $b < 0$ and discriminant $∆ = h^2 - 4abk < 0$
  • $b > 0$ and discriminant $∆ = h^2 - 4abk < 0$
  • $b > 0$ and discriminant $∆ = h^2 - 4abk > 0$
  • $b < 0$ and discriminant $∆ = h^2 - 4abk > 0$ (correct)

    • What does it mean if the leading coefficient $b$ in the quadratic equation $f(x) = abx$ is not equal to 1?

  • The vertex of the parabola is at $(0, a)$
  • The parabola is wider if $|b|$ is smaller
  • The parabola opens upwards if $b > 0$ and downwards if $b < 0$ (correct)
  • The $x$-intercepts are at $(a, 0)$ and $(-a, 0)$

    • If $a eq 0$ in the quadratic equation $f(x) = abx$, what can be said about the $x$-intercepts?

  • The $x$-intercept is at $(0, 0)$ (correct)
  • The $x$-intercept is at $(a, 0)$
  • The $x$-intercept is at $(0, a)$
  • There are no $x$-intercepts

    • For the quadratic equation $f(x) = 9x^2 - 4x - 3$, what are the roots of the equation?

    <p>$x = 3$ and $x = -\frac{1}{3}$</p> Signup and view all the answers

    What does the value of the discriminant $∆$ indicate about the roots of a quadratic equation?

    <p>All of the above</p> Signup and view all the answers

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