A nonlinear function that can be written on the standard form
<span><span>a<span>x2</span>+bx+c,wherea≠0</span><span>a<span>x2</span>+bx+c,wherea≠0</span></span>
is called a quadratic function.
All quadratic functions has a U-shaped graph called a parabola. The parent quadratic function is
<span><span>y=<span>x2</span></span><span>y=<span>x2</span></span></span>
The lowest or the highest point on a parabola is called the vertex. The vertex has the x-coordinate
<span><span>x=−<span>b<span>2a</span></span></span><span>x=−<span>b<span>2a</span></span></span></span>
The 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 <span>x2</span>we 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 equation
<span><span>x=−<span>b<span>2a</span></span></span><span>x=−<span>b<span>2a</span></span></span></span>
The 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.
