How do you graph a quadratic equation?

Answer 1

A quadratic equation is an equation with the form:

y=Ax2+Bx+C

The most important point when graphing a parabola (the shape formed by a quadratic) is the vertex. The vertex is the maximum or minimum of the parabola.

The x value of the vertex is equal to -B/(2A). Once you have the x value, just plug it back into the original equation to get the corresponding y value. The resulting ordered pair is the location of the vertex.

A parabola will be concave up (pointed downward) if A is +. It will be concave down (pointed upward) if A is -.

It is often helpful to find the zeroes of a function when graphing. This can be done by factoring or using the quadratic formula.

For every n units away from the vertex on the x-axis, the corresponding y value goes up (or down) by n2*A. Parabolas are symetrical along the vertex, which means that if one point is n units from the vertex, the point -n units from the vertex has the same y value.

As an example take the following quadratic: 2x2-8x+3

A=2, B=-8, and C=3

The x value of the vertex is -B/2A=-(-8)/(2*2)=2

By plugging 2 into the original equation we get that the vertex is at (2,-5)

3 units to the right (x=5) has a y value of -5+32*2=13. This means that 3 units to the left (x=-1) has the same y value (-1,13).

If you need a clearer explanation, ask a math teacher.