Quadratic functions and their graphsEdexcel International A Level Maths: Subtopic test

1. 1
   The quadratic function $f(x)=x^2-6x+5$.

   (a)

   Which point is where the graph of $y=f(x)$ crosses the $y$-axis?

   [1 mark]

   • A$(0,5)$
   • B$(5,0)$
   • C$(0,-5)$
   • D$(0,-6)$

   (b)

   At which values of $x$ does the graph of $y=f(x)$ cross the $x$-axis?

   [1 mark]

   • A$x=-1$ and $x=-5$
   • B$x=1$ and $x=5$
   • C$x=2$ and $x=3$
   • D$x=-1$ and $x=5$

   (c)

   Find the coordinates of the minimum point of the graph of $y=f(x)$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A curve $C$ has equation $y=-2x^2+8x-3$.

   (a)

   What is the equation of the line of symmetry of $C$?

   [1 mark]

   • A$x=2$
   • B$x=-2$
   • C$x=4$
   • D$x=-4$

   (b)

   What is the maximum value of $y$ on $C$?

   [1 mark]

   • A$-3$
   • B$21$
   • C$5$
   • D$2$

   (c)

   The line $y=-3$ meets $C$ at two points. Find the $x$-coordinates of these points.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A quadratic function is $f(x)=2x^2+px+q$, where $p$ and $q$ are constants. The graph of $y=f(x)$ crosses the $x$-axis at $x=-1$ and $x=\frac52$.

   (a)

   Find the values of $p$ and $q$.

   [3 marks]

   (b)

   Find the coordinates of the turning point of the graph of $y=f(x)$ and state whether it is a maximum or a minimum.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A stone is thrown upwards from a bridge over a river. Its height $h$ metres above the river, $t$ seconds after it is thrown, is modelled by $h=-5t^2+20t+25$ for $0\le t\le T$, where $T$ is the time at which the stone enters the water.

   (a)

   (i) Find the height of the bridge above the river.
   (ii) Find the maximum height of the stone above the river and the time at which it is reached.
   (iii) Find the value of $T$.

   [6 marks]

   (b)

   A drone hovers at a height of $40$ m above the river. Find the length of time for which the stone is higher than the drone, and explain how the shape of the graph of $h$ against $t$ shows which values of $t$ you need.

   [6 marks]

   Total for question 4: 12 marks

End of questions