In quadratic equations, we often write them like this: ( ax^2 + bx + c = 0 ). The letters ( a ), ( b ), and ( c ) are important because they help us understand what the graph of the equation looks like, especially the shape called a parabola.

1. Coefficient ( a ):

• This number decides which way the parabola opens:
  • If ( a > 0 ) (a positive number), the parabola opens upwards.
  • If ( a < 0 ) (a negative number), it opens downwards.
• It also changes how wide or narrow the parabola is:
  • Bigger numbers for ( |a| ) (the absolute value of ( a )) make the graph narrower.
  • Smaller numbers for ( |a| ) make the graph wider.

2. Coefficient ( b ):

• This number helps find where the top or bottom point (called the vertex) of the parabola is located on the x-axis.
• We can use the formula ( x = -\frac{b}{2a} ) to find this point.
• Knowing where the vertex is helps us find the highest or lowest point of the quadratic function.

3. Coefficient ( c ):

• This number shows us where the parabola crosses the y-axis.
• We can find that point at ( (0, c) ) on the graph.

Knowing about these coefficients makes it easier to understand and draw quadratic equations. This is really important for Year 10 Mathematics!