Quadratic Graphs – GCSE Mathematics (Higher) OCR Revision

Understanding Quadratic Graphs

Quadratic graphs: curves that are produced by quadratic equations, which are polynomials of degree 2 in the form y = ax² + bx + c.
Turning point (or vertex): the highest or the lowest point on the graph of a quadratic function. This point is where the graph changes direction.
Axis of symmetry: the vertical line that cuts the parabola (the shape of a quadratic graph) in half.
Roots: where the graph intersects the x-axis. Sometimes called zeros.
Parabola: The U-shape curve of a quadratic graph. If ‘a’ is positive in a quadratic equation, the parabola opens upwards. If ‘a’ is negative, it opens downwards.

A typical quadratic equation is in the form y = ax² + bx + c where a ≠ 0.
A function is quadratic if the highest power of x is 2.
Quadratic graphs always form a parabola, and the parabola will either face up or down depending on whether ‘a’ is positive or negative.
Changing the values of ‘a’, ‘b’ or ‘c’ in the quadratic equation will change the position and shape of the graph.
The vertex or the turning point of the parabola can be calculated using the formula (-b/2a , f(-b/2a)) where f(x) is the quadratic function.
The roots of a quadratic equation are where y = 0. These are the x-coordinates where the parabola crosses the x-axis.
The axis of symmetry of a parabolic graph can be found using the formula x = -b/2a.

Before sketching a graph, identify the vertex, axis of symmetry and roots if possible.
Plot the vertex and roots first and then use symmetry to draw the rest of the graph.
Remember, the graph of a quadratic equation always forms a parabola.

Quadratic graphs are used to model various phenomena in physics, engineering, business, and in calculating the trajectory of projectiles.
Understanding quadratic graphs is also essential for many fields such as data analysis and machine learning.

Remember to always check your work and ensure your answers make sense in the context of the question.