How do you graph a quadratic equation? (parabolas)?

Question

Like how do you find the point of symmetry or whatever and the other points
And what is -b/2a for?

Answer 1

For a quadratic function
f(x) = ax^2 + bx + c

-b/(2a) indicates the x-coordinate of a parabola's vertex. The y-coordinate is given by f(-b/(2a))

The general method in graphing a parabola is as follows:
(1) Find the x-intercepts and y-intercept, if any
(2) Find the vertex.

The vertex will determine the minimum or maximum point of a parabola. Therefore it should be trivial to graph given those points.

Answer 2

Common equation: y= ax(exp2) + bx + c

-b/2a comes from the quadratic equation, when the terms under the root are equal to zero (ie. exactly one real root and no imaginary roots).

Real roots are the points at which the graph of the parabola crosses the x-axis. this means that -b/2a gives you your y=0 value, x-intercept.

Draw a two-column chart with x and y columns. Start with x=0 and solve equation. Then try a few more numbers, typically a minimum of three. Then sketch in your graph.

Point of symmetry (or line of symmetry) is where graph fulfills the equation: 0 =ax(exp2) + bx + c (ie. when y=0)