Graphs and Graphical Solution of Quadratic Equations 1

1. Quadratic graphs are graphs whose equations are of the form y = ax2 + bx + c, where a, b and c are constants and a ≠ 0. (This is because if a = 0, then the equation becomes y = bx + c which is a linear graph!)
2. The graph of a quadratic equation is a smooth U-shaped curve called a parabola.
3. The curve of a quadratic graph is symmetrical about the line of symmetry.
4. The curve of a quadratic graph has either a maximum or a minimum point. The line of symmetry passes through the maximum/minimum point of the parabola. 
5. To sketch the graph of a quadratic equation, rewrite the equation in the form y = ± (x - p)2 + q or y = (x - a)(x - b) where a, b, p and q are constants. 

For the form of  y = ± (x - p)2 + q, (p, q) will be the coordinates of the maximum/minimum point while x = p will be the equation of the line of symmetry.

Graphs and Graphical Solution of Quadratic Equations 2

For the form of y = (x - a)(x - b), x = (a+b)/2 is the equation of the line of symmetry, while a and b are the x-intercepts of the graph, as illustrated below:

Gradient

Tangent refers to a line that touches the graph at one and only one point. It can aid us in calculating the gradient of the curve at that particular point, as seen from the image below:

Answering Technique

Do note the following: