Quadratic Inequalities (HSC SSCE Mathematics Advanced): Quizzes

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Quadratic Inequalities
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What does a quadratic inequality compare?

A quadratic function to a constant/function

In f(x)=ax2+bx+cf(x) = ax^2 + bx + c, what must be true about aa?

a≠0a \neq 0

What is the first step in the algebraic method for solving quadratic inequalities?

Find boundary points by solving equation

What is the discriminant formula for a quadratic equation?

Δ=b2−4ac\Delta = b^2 - 4ac

If Δ>0\Delta > 0, how many boundary points exist?

Two distinct boundary points

Which inequality symbols indicate boundary points should be included in the solution?

≤\leq or ≥\geq

For f(x)>kf(x) > k, where is the parabola relative to the line y=ky = k?

Above the line

What type of values form the solution to a quadratic inequality?

A range or ranges of x-values

If (x−5)(x+1)=0(x - 5)(x + 1) = 0, what are the boundary points?

x=5x = 5 or x=−1x = -1

What is the purpose of testing intervals in the algebraic method?

To check which intervals satisfy inequality

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