Quadratic Graphs
Quadratic Graphs Basics
 A quadratic graph is a curve called a parabola.
 The general formula for a quadratic equation is y = ax^2 + bx + c.
 The xcoordinate of the vertex of the parabola is given by b/2a.
 The discriminant (b^2  4ac) determines the number of xintercepts of the graph.
 If the discriminant is positive, the graph will intersect the xaxis at two different points. If it’s zero, the graph will touch the xaxis at one point. If it’s negative, the graph will not intersect the xaxis at all.
Understanding Quadratic Graphs Key Features
 The vertex of the graph is its highest or lowest point, depending on its orientation.
 The axis of symmetry divides the graph into two mirror images.

The coefficient ‘a’ affects the direction and width of the parabola. If ‘a’ is positive, the graph opens upwards. If ‘a’ is negative, the graph opens downward. Larger a values make the graph thinner, and smaller a values make it wider.  The yintercept is at the point (0, c) where ‘c’ is the constant term in the formula.
Plotting Quadratic Graphs
 When plotting a quadratic graph, start by identifying the key points such as the vertex and yintercept.
 Use the axis of symmetry and other identified points to reflect and plot the other half of the graph.
 Remember to draw smooth, curved lines to represent the graph, with arrows at the end to indicate that the graph extends indefinitely.
Transformations of Quadratic Graphs
 Shifts upwards or downwards are caused by changes in the constant term, ‘c’.
 Shifts to the left or right occur due to transformations of ‘x’ within the squared term.
 Reflections in the xaxis are the result of the square term being negated.
Studying and practicing these points will strengthen your understanding of quadratic graphs, thus fortifying your grasp on Algebraic skills.