Higher Homework
Quadratic Functions
Q1. Sketch the graph of f(x) = x2 – 2x – 15 showing the y – intercept, roots and turning point.
Q2. Write the following in completed square form: a(x + p)2 + q
(i)
x2 – 4x + 13
(ii) 5 + 16x – x2
(iii) 2x2 + 12x – 3
Q3. For what value of k does the equation 2x2 – 7x + k + 5 = 0 have equal roots?
Q4. Show that the line y = 2x – 21 is a tangent to the parabola y = x2 - 10x + 15 and find the
point of contact.
Q5. Show that the line y = 2x + 1 does not intersect the parabola with equation y = x2 + 3x + 4
Q6. Find the equation of the parabola that passes through the points (-4, 0) (2, 0) and (0, -16)
Q7. The roots of the equation (x + 1)(x + k) = -4 are equal. Find the values of k
Q8. The parabola shown in the diagram has equation y = x2 – 4x - 5 and intersects the y-axis at
the C.
The line CD has equation x + y = -5
Find the coordinates of the points C and D.