A nonlinear function that can be written on the standard form
ax2+bx+c,wherea≠0ax2+bx+c,wherea≠0is called a quadratic function.All quadratic functions has a U-shaped graph called a parabola. The parent quadratic function isy=x2y=x2
The lowest or the highest point on a parabola is called the vertex. The vertex has the x-coordinatex=−b2ax=−b2aThe y-coordinate of the vertex is the maximum or minimum value of the function.a > 0 parabola opens up minimum value
a < 0 parabola opens down maximum value
A rule of thumb reminds us that when we have a positive symbol before x2we get a happy expression on the graph and a negative symbol renders a sad expression.The vertical line that passes through the vertex and divides the parabola in two is called the axis of symmetry. The axis of symmetry has the equationx=−b2ax=−b2aThe y-intercept of the equation is c.
When you want to graph a quadratic function you begin by making a table of values for some values of your function and then plot those values in a coordinate plane and draw a smooth curve through the points.