Question

How do you graph `F(x)=3x^2+4x-1`?

Answer 1

Find the vertex and plot some "nice" points around that point.

Explanation:

`y=3x^2+4x-1`
`a=3, b=4, and c=-1`
The vertex is at `x_v=-b/(2a)=-4/6=-2/3`
The corresponding y value is at
`y_v=3(-2/3)^2+4(-2/3)-1=4/3-8/3-3/3=-7/3`

Find some "nice" values of x that are around the vertex.

`f(-2)=12-8-1=3`
`f(-1)=3-4-1=-2`
`f(0)=0+0-1=-1`
`f(1)=3+4-1=6`

Plot the points `(-2,3), (-1,-2),(-2/3,-7/3),(0,-1), and (1,6)` and sketch in the graph. graph{3x^2+4x-1 [-3, 1.2, -4, 7]}

Answer 2

show the perfect answer below

Explanation:

show the steps

For example `ax^2+bx+c=0`

A nonlinear function that can be written on the standard form

`ax^{2}+bx+c,\: \: where\: \: a\neq 0`
is called a quadratic function.

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

`y=x^2`

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

`x=-\frac{b}{2a}`

The y-coordinate of the vertex is the maximum or minimum value of the function.

`a>0` parabola opens up

`a<0` parabola opens down

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=-\frac{b}{2a}`

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.

now we will graph

`F(x)=3x^2+4x-1`

donot forget Make a table of value for some values of x. Use both positive and negative values!

That will help you in sketch.