"Not a lot of people know this, but I'm very good at mathematics. When I was an angry teenager, I used to sit in my room and do quadratic equations to calm myself down "
Samantha Bond
1. The quadratic graph \( y = a(x - p)(x - q) \) crosses the \( x \)-axis at \( (p,0) \) and \( (q,0) \). The quadratic graph \( y = a(x - h)^2 + k \) has vertex \( (h,k) \) and line of symmetry \( x = h \).
2. You should be able to complete the square: \[ x^2 + bx + c = \left(x + \frac{b}{2}\right)^2 - \left(\frac{b}{2}\right)^2 + c. \]
3. You should be able to solve quadratic equations by factorizing, completing the square, and using the quadratic formula. If \( ax^2 + bx + c = 0 \), then \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. \]
4. You should be able to solve quadratic inequalities.
5. You should be able to use the discriminant \( \Delta \) to determine the
number of roots of a quadratic equation, where
\( \Delta = b^2 - 4ac \).
If \( \Delta > 0 \), there are two distinct real roots;
if \( \Delta = 0 \), there are two equal real roots;
and
if \( \Delta < 0 \), there are no real roots.
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