Q1. The graph of $y = p(x)$ is given below. The number of zeroes of $p(x)$ is:
Q2. Which of the following is not the graph of a quadratic polynomial?
Q3. If the graph of a quadratic polynomial $ax^2 + bx + c$ opens downwards, then:
Q4. Assertion (A): The graph of $y = x^2 + 1$ does not intersect the x-axis. Reason (R): The discriminant of $x^2 + 1$ is negative ($D < 0$).
Q5. Look at the graph below. Identify the zeroes of the polynomial.
Solve on white paper.
Q6. Draw a rough sketch of the graph of the polynomial $p(x) = x^2 - 4$.
Q7. If the graph of a polynomial intersects the x-axis at exactly one point, does it imply that it is a linear polynomial? Justify.
Q8. The graph of a quadratic polynomial $y = ax^2 + bx + c$ passes through the points $(-1, 0)$, $(3, 0)$ and cuts the y-axis at $(0, -3)$. Find the polynomial.
Q9. Find the zeroes of the polynomial $p(x) = x^2 - 3x - 4$ graphically.
Q10. Consider the polynomial $p(x) = -x^2 + 2x + 3$.
(i) Determine the direction in which the parabola opens.
(ii) Find the zeroes of the polynomial.
(iii) Find the coordinates of the vertex.
(iv) Draw the graph.
Q11. Case Study: Projectile Motion
A soccer player kicks a ball. The path of the ball can be modelled by the quadratic polynomial $h(t) = -t^2 + 6t$, where $h(t)$ is the height in meters at time $t$ seconds.
(i) What is the shape of the path of the ball?
(ii) At what time does the ball hit the ground again?
(iii) What is the maximum height achieved by the ball?