Q1: What is the general form of a quadratic equation?
ax^2+bx+c=0
Q2: What does “factorisation” mean in solving quadratics?
Rewriting the quadratic as
(x−p)(x−q)=0 to find roots.
Q3: What is the purpose of completing the square?
A3: To rewrite a quadratic in vertex form to make solving and graphing easier.
Q5: What are simultaneous equations?
A5: A set of equations solved together for the same variables.
Q7: What is meant by “quadratic in form”?
A7: An equation that becomes quadratic after substitution.
Q6: What type of graph can represent a quadratic equation?
A6: A parabola (or more generally, a conic).
Q7: What method is used to solve when combining a linear and quadratic equation?
A7: Substitution method.
Q8: After substitution, how do you solve the quadratic?
A8: By factorising or using the quadratic formula.
Q9: What does “quadratic in form” mean?
A9: An equation that becomes quadratic after substitution.
Q10: What method is often used to simplify such equations?
A10: Substitution method.
Q11: After substitution, what is the next step?
A11: Factorisation or quadratic formula.
Q12: What shape is the graph of a quadratic function?
A12: A parabola.
Q13: What is the vertex of a parabola?
A13: The turning point (maximum or minimum).
Q14: What is another name for a turning point?
A14: Stationary point.
Q15: What line passes through the vertex of a parabola?
A15: The line of symmetry.
Q16: If a>0, what point does the parabola have?
A16: Minimum point.
Q17: If a<0, what point does the parabola have?
A17: Maximum point.
Q18: What is a quadratic inequality?
A18: An inequality involving a quadratic expression, e.g.
ax^2+bx+c>0.
Q19: Which intercepts are important for solving quadratic inequalities?
A19: X-intercepts and Y-intercepts.
Q20: What expression determines the number of roots?
A20: The discriminant,
b^2−4ac.
Q21: What does it mean if the discriminant is positive?
A21: Two distinct real roots.
Q22: What does it mean if the discriminant equals zero?
A22: Two equal real roots (a repeated root).
Q23: What does it mean if the discriminant is negative?
A23: No real roots.
Q24: How many points of intersection are possible between a line and a quadratic curve?
A24: Two, one, or none.
