1Solve by the graphical method: (a) \( x^2 + 2x - 3 = 0 \)
2Solve by the graphical method: (b) \( x^2 - 5x + 6 = 0 \)
3Solve by the graphical method: (c) \( x^2 - 4x + 3 = 0 \)
4Solve by the graphical method: (d) \( 2x^2 - 7x + 3 = 0 \)
5Solve by the graphical method: (e) \( x^2 - 3x - 10 = 0 \)
6Solve the pair of equations by graph: (a) \( y = x^2 \) and \( y = x + 2 \)
7Solve the pair of equations by graph: (b) \( y = x^2 - x - 3 \) and \( x - y = 0 \)
8Solve the pair of equations by graph: (c) \( y = 6x^2 - 2x - 15 \) and \( y = 4x - 3 \)
9Solve the pair of equations by graph: (d) \( y = x^2 - 2x \) and \( y = x + 4 \)
10Find the equation of the parabola (a), which passes through \( (-4, 2) \), \( (-3, 0) \), \( (-2, 0) \) and \( (-1, 2) \).
11Find the equation of the parabola (b), which passes through \( (-4, 0) \), \( (3, 0) \), \( (-2, -10) \) and \( (1, -10) \).
12Find the equation of the parabola (c), which passes through \( (-3, 9) \), \( (4, 9) \), \( (-1, -1) \) and \( (2, -1) \).
13Find the equation of the parabola (d), which passes through \( (-5, 7) \), \( (3, 7) \), \( (-2, -8) \) and \( (0, -8) \).
14Why do Method 1 and Method 2 always give the same solutions for a quadratic equation?
15Show by a graph that \( x^2 - 4x + 7 = 0 \) has no real solution.
16Solve \( x^2 + 2x + 1 = 0 \) by graph and say what is special about the result.
17A parabola passes through \( (1, 0) \), \( (3, 0) \) and \( (0, 3) \). Find its equation.