Question

how do i graph
y=3x^2+7x+2

Answer 1

What tools do you have?

Algebra 1 - Plotting Points
Algebra II/Analytic Geometry - Vertex Form of Parabola
Calculus - Critical Points
CAS - Get a computer to do it for you.

Answer 2

algebra 2

Answer 3

Perfect, then you'll need to complete the square on the right hand side.

Answer 4

y=3x^2+7x+2

I'll do it once for free if you're rusty.

Answer 5

i know that in the graph we have a x and a y intercept right

Answer 6

That's a good place to start. The y-intercept is easy. Just substitute x = 0 and get y = 2. Done!

x-interecpts are a little harder, requiring factoring or the quadratic formula (or completing the square)

Answer 7

I prefer two more things before that, though.

x is squared and y is linear. This gives a parabola that opens either up or down.
The coefficient on x^2 is positive (3), so this one opens up!

There, that makes me feel better.

Answer 8

There is also an easy way to find the axis of symmetry (a direct result of completing the square, actually.)

Answer 9

You are in very capable hands, stick with tkhunny and learn.

Answer 10

so how do i graph if the vertex is -7/6

Answer 11

So, you DO know the magic -b/(2a)!

Just find the value of y associated with x = -7/6

With a vertex, 2 x-intercepts, a y-intercept, and some idea about symmetry you should be good to go!

Answer 12

but how do i graph it

Answer 13

whats my next step

Answer 14

Where are all the points you had catalogued?