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

2 Answers
Apr 28, 2018

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]}

Apr 29, 2018

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#

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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

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#a<0# parabola opens down

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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.

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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#

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

That will help you in sketch.