AS Pure Chapter 2: Quadratics

12 flashcards · Mathematics · by TheoTyson

1. How many solutions can a quadratic have?

   1,21, 21,2 or 000 solutions.

2. How can you solve a quadratic by factorising?

   Factorise the quadratic and set each factor equal to 000 to find the values of xxx .

3. What is the quadratic formula?

   x=−b±b2−4ac2ax = \frac{-b ± \sqrt{b^2 - 4ac}}{2a}x=2a−b±b2−4ac ​​

4. What is the domain of a function?

   Possible inputs for a function.

5. What is the range of a function?

   Possible outputs for a function.

6. What are the roots of a function?

   The values of xxx for which f(x)\text{f}(x)f(x) = 000 .

7. What does x∈Rx \in \Rx∈R mean?

   xxx belongs to the set of all real numbers.

8. What are the coordinates of the turning point of a quadratic with equation f(x)=a(x +p)2+q\text{f}(x) = a(x \, + p)^2 + qf(x)=a(x+p)2+q

   Turning point at (−p,q)(-p, q)(−p,q)

9. What is the value of the discriminant of a quadratic function?

   b2−4acb^2 - 4acb2−4ac

10. What does 0"> b2−4ac>0b^2 - 4ac > 0b2−4ac>0 mean?

    Two real roots.

11. What does b2−4ac=0b^2 - 4ac = 0b2−4ac=0 mean?

    One repeated root.

12. What does b2−4ac<0b^2 - 4ac < 0b2−4ac<0 mean?

    No real roots.