Quadratic Equations Exam Prep
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Quadratic equations
Sample questions with model answers
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Discuss the applications of quadratic equations in real life.
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Quadratic equations model projectile motion, area problems, and profit maximization in business.
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Solve the quadratic equation $2x^2 - 4x - 6 = 0$ using the quadratic formula.
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Using $x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4 \cdot 2 \cdot (-6)}}{2 \cdot 2}$, the roots are $3$ and $-1$.
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Differentiate between the roots of a quadratic equation when the discriminant is positive, zero, and negative.
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Positive $D$: two distinct real roots; Zero $D$: one real root; Negative $D$: no real roots.
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Graph the quadratic function $y = ax^2 + bx + c$ and identify its vertex.
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The vertex is at $x = -\frac{b}{2a}$; plot the parabola opening up or down based on $a$.
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