Quadratic Functions: Practice Questions with Answers

This page contains a collection of practice questions on quadratic functions. The questions focus on key concepts such as the vertex, axis of symmetry, maximum and minimum values, intervals of increase and decrease, and the range of a quadratic function.

Questions

Question 1

Find the maximum or minimum value of the function \[ f(x) = 2x^2 + 3x - 5. \]

Question 2

Find the range of the function \[ f(x) = -x^2 + 4x - 5. \]

Question 3

Find the vertex of the graph of \[ f(x) = 3x^2 + 6x - 10. \]

Question 4

Find the intervals of increase and decrease of \[ f(x) = 6x^2 + x - 2. \]

Question 5

Find the axis of symmetry of the graph of \[ f(x) = -2x^2 - x - 2. \]

Question 6

Find the maximum or minimum value of \[ f(x) = -3x^2 + 9x. \]

Question 7

Find the range of \[ f(x) = x^2 + 5x - 2. \]

Question 8

Find the vertex of the graph of \[ f(x) = -x^2. \]

Question 9

Find the intervals of increase and decrease of \[ f(x) = -\frac{1}{2}x^2 + 1.1x - 2.3. \]

Question 10

Find the axis of symmetry of the graph of \[ f(x) = -\frac{1}{2}x^2 + 1.1x - 2.3. \]

Question 11

Find the range of \[ f(x) = -(x - 2)^2 + 2x + 4. \]

Question 12

Find the vertex of the graph of \[ f(x) = -(x + 4)^2 + 4x - 2. \]

Question 13

Find the equation of the quadratic function \(f\) whose maximum value is \(-3\), whose axis of symmetry is given by \(x = 2\), and such that \(f(0) = -9\).

Question 14

Find the equation of the quadratic function \(f\) whose graph increases on the interval \(( -\infty, -2 )\), decreases on the interval \(( -2, +\infty )\), and satisfies \(f(0) = 23\) and \(f(1) = 8\).

Question 15

Find the equation of the quadratic function \(f\) whose minimum value is \(2\), whose axis of symmetry is given by \(x = -3\), and such that \(f(2) = 1\).

Answers

1. The function has a minimum value equal to \[ -\frac{49}{8}. \]

2. The range of the function is \[ ( -\infty, -1 ]. \]

3. The vertex of the graph is at \[ (-1, -13). \]

4. The function decreases on \[ ( -\infty, -\tfrac{1}{12} ) \] and increases on \[ ( -\tfrac{1}{12}, +\infty ). \]

5. The axis of symmetry is the vertical line \[ x = -\frac{1}{4}. \]

6. The function has a maximum value equal to \[ \frac{27}{4}. \]

7. The range of the function is \[ \left[ -\frac{33}{4}, +\infty \right). \]

8. The vertex of the graph is at \[ (0, 0). \]

9. The function increases on \[ ( -\infty, 1.1 ) \] and decreases on \[ ( 1.1, +\infty ). \]

10. The axis of symmetry is the vertical line \[ x = 1.1. \]

11. The range of the function is \[ ( -\infty, 9 ]. \]

12. The vertex of the graph is at \[ (-2, -14). \]

13. The quadratic function is \[ f(x) = -\frac{3}{2}(x - 2)^2 - 3. \]

14. The quadratic function is \[ f(x) = -3(x + 2)^2 + 35. \]

15. Such a quadratic function does not exist, since \(f(2) = 1\) is smaller than the given minimum value \(2\).