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 x-coordinate of the vertex of the parabola is given by -b/2a.
• The discriminant (b^2 - 4ac) determines the number of x-intercepts of the graph.
• If the discriminant is positive, the graph will intersect the x-axis at two different points. If it’s zero, the graph will touch the x-axis at one point. If it’s negative, the graph will not intersect the x-axis 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 y-intercept 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 y-intercept.
• 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 x-axis 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.