Quadratic Equations quiz

More questions about Quadratic Equations

These visible examples show the question style. LearnClash turns the full topic into ranked duels and spaced repetition.

1. 1 Easy

   What is $b^2-4ac$ called?

   Answer: Discriminant

   Why: Its sign sorts every quadratic into cases: positive gives two real roots, zero gives one, negative gives no real roots.

2. 2 Medium

   Where does $y=(x-3)^2$ move the graph of $y=x^2$?

   Answer: 3 units right

   Why: The bracket is zero at $x=3$, so the vertex moves there: a minus inside the bracket means a shift right.

3. 3 Hard

   How many standard equation types does al-Khwarizmi's book list?

   Answer: 6

   Why: Every coefficient had to be positive, so $ax^2+bx=c$, $ax^2+c=bx$ and $bx+c=ax^2$ count as three different types.

4. 4 Easy

   Who solved quadratic problems on clay tablets by 1800 BC?

   Answer: Babylonians

   Why: Egyptian scribes solved one too: the Berlin Papyrus, from roughly the same era, works out a simple two-term quadratic.

5. 5 Medium

   How much do you add to $x^2+10x$ to make a perfect square?

   Answer: 25

   Why: Al-Khwarizmi's own example works this way: $x^2+10x=39$ becomes $(x+5)^2=64$, so $x=3$.

6. 6 Hard

   How far apart are the real roots of $x^2+bx+c=0$?

   Answer: $\sqrt{b^2-4c}$

   Why: Slide the parabola sideways and both roots move together, yet $b^2-4c$, and with it the gap, stays exactly the same.