MATHEMATICS Quadratic Functions Date: 2nd March 2010 Student name: Class: MYP 4 The equation of a “quadratic function” is given by y = ax2 + bx + c, where a ≠ 0, and the graph of a quadratic function is called a parabola. If the coefficient of “x2” is positive, then the graph opens upwards, and if it is negative then the graph opens downwards as shown below. Quadratic graphs positive quadratic y = x2 Page 1 of 3 negative quadratic y = –x2 Date of issue: 11-Mar-19 -The point of intersection with the y-axis, where x = 0 is the y-intercept. -The points of intersection with the x-axis, where y = 0 are called the x-intercepts, the ZEROS of the function or roots of the equation. - The vertex is the ‘turning point’ or the point at which the parabola changes its direction. [It can be minimum or maximum] - The x coordinate of the vertex is equal to: and is also the midpoint of the roots (zeros) of the equation, and the y-coordinate can be calculated by substituting with the x-coordinate in the equation. -The vertical line that passes through the vertex is called the axis of symmetry Quadratic Graphs Page 2 of 3 Date of issue: 11-Mar-19 Draw the graphs of the following functions using a scale of 2cm for 1 unit on the x-axis and 1cm for 1 unit on y-axis. For each graph state the following: a) The y-intercept b) The zeros of the equation c) The equation of the axis of symmetry d) The coordinates of the vertex and whether it is a maximum or minimum point 1. y = x2 + x – 2 , for -3 ≤ x ≤ 3 2. y = x2 +3x – 9 , for -4 ≤ x ≤ 3 3. y = x2 – 3x – 4 , for -2 ≤ x ≤ 4 4. y = 2 + x - x2 , for -3 ≤ x ≤ 3 5. y =3 + 3x - x2, for -2 ≤ x ≤ 5 6. y = 7 – 3x - 2x2, for -3≤ x ≤ 3 Quadratic Graphs Page 3 of 3 Date of issue: 11-Mar-19