Cards In This Deck

• $\text{If a quadratic function is written as }f(x)=a(x+p{)}^2+q\text{, what are the coordinates of the turning point?}$
  $(-p,q)$
• $\text{Condition for the function }f(x)=a{x}^2+bx+c\text{ to have a maximum turning point?}$
  $a<0$
• $\text{To find the coordinates of the turning point of }y=2x^2-12x+7\text{, which method is most direct?}$
  $\text{Completing the square.}$
• $$\begin{gathered} \text{True or False?} \\ \text{The roots of a function }f(x)\text{ are the values of }x\text{ where }f(x)\text{ crosses the y-axis.} \end{gathered}$$
  $$\begin{gathered} \text{False} \\ \text{Correct Answer: The roots are where }f(x)\text{ crosses the x-axis (where }f(x)=0\text{).} \end{gathered}$$
• $$\begin{gathered} \text{True or False?} \\ \text{If }{b}^2-4ac=0\text{, the quadratic equation has no solutions.} \end{gathered}$$
  $$\begin{gathered} \text{False} \\ \text{Correct Answer: It has one repeated real root.} \end{gathered}$$
• $$\begin{gathered} \text{True or False?} \\ \text{The condition for a quadratic to have "real roots" is }{b}^2-4ac>0\text{.} \end{gathered}$$
  $$\begin{gathered} \text{False} \\ \text{Correct Answer: }{b}^2-4ac\ge 0 \end{gathered}$$
• $\text{Condition for the quadratic equation }{x}^2+kx+9=0\text{ to have equal roots.}$
  $b^2-4ac=0\Rightarrow k^2-4(1)(9)=0$
• $\text{When checking how many times the line }y=2x+1\text{ intersects the curve }y=x^2\text{, what should you calculate first?}$
  $\text{Substitute the line equation into the curve equation to form a single quadratic: }{x}^2=2x+1\Rightarrow x^2-2x-1=0\text{.}$
• $\text{Write the formula for the Discriminant.}$
  $b^2-4ac$
• $\text{Condition for a quadratic equation to have two distinct real roots.}$
  $b^2-4ac>0$
• $\text{Condition for a quadratic equation to have equal roots (one repeated root).}$
  $b^2-4ac=0$
• $\text{Condition for a quadratic equation to have no real roots.}$
  $b^2-4ac<0$
• $$\begin{gathered} \text{True or False?} \\ \text{Completing the square for }2x^2+8x+1\text{ starts by writing }2(x+2{)}^2... \end{gathered}$$
  $\text{False}$
• $\text{When solving a quadratic equation like }3x^2-7x-1=0\text{, why might you choose the Quadratic Formula over factorising?}$
  $\text{The expression }3x^2-7x-1\text{ cannot be easily factorised into integers (its discriminant is not a perfect square).}$
• $\text{Write the Quadratic Formula for solving }a{x}^2+bx+c=0\text{.}$
  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
• $\text{What is the first step to complete the square for }3x^2+6x+1\text{?}$
  $\text{Factorise the coefficient of }{x}^2\text{ out of the }x\text{ terms: }3(x^2+2x)+1\text{.}$
• $\text{What is the crucial first step before identifying }a,b,c\text{ for the Quadratic Formula?}$
  $\text{Rearrange the equation to the form }a{x}^2+bx+c=0\text{.}$