Worksheets · Foundation and Higher

Quadratic graphs, roots and turning points

3 exam-style questions. Answers and the mark for each step are on the last page.

1. Question 1Non-calculator · 2 marks

   Here is the equation of a curve: $y = x^2 + 1$.

   (a) Work out the value of $y$ when $x = -2$. (1)

   (b) Which point is the turning point of the curve? (1)

   1. $(0, 1)$
   2. $(1, 0)$
   3. $(0, 0)$
2. Question 2Non-calculator · 4 marks

   A ball is thrown from ground level. Its height, h metres, after t seconds is $h = 12t - 3t^2$ for $0 \le t \le 4$.

   (a) Find the two times when the ball is at ground level. (2)

   (b) Find the greatest height of the ball. (2)
3. Question 3Non-calculator · 5 marks

   The curve $y = (x - 3)(x + 5)$ is a parabola.

   (a) Write down the coordinates of the points where the curve crosses the $x$-axis. (1)

   (b) Find the coordinates of the turning point of the curve. (3)

   (c) For which value of $k$ does the equation $(x - 3)(x + 5) = k$ have exactly one solution? (1)