Question

Why quadratic equation is ax^2+bx+c=y ?

Answer 1

Step-by-step explanation:

nonlinear function that can be written on the standard form

ax2+bx+c,wherea≠0ax2+bx+c,wherea≠0

is called a quadratic function.

All quadratic functions has a U-shaped graph called a parabola. The parent quadratic function is

y=x2y=x2

The lowest or the highest point on a parabola is called the vertex. The vertex has the x-coordinate

x=−b2ax=−b2a

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 x2 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

x=−b2ax=−b2a

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.

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