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What are the conditions for the quadratic equation $f(x) = abx-h ± k$ to have real roots?
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?
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?
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?
For the quadratic equation $f(x) = 9x^2 - 4x - 3$, what are the roots of the equation?
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What does the value of the discriminant $∆$ indicate about the roots of a quadratic equation?
What does the value of the discriminant $∆$ indicate about the roots of a quadratic equation?
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