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Graphing a function
- Thread starter SWood
- Start date
arthur ohlsten
Full Member
- Joined
- Feb 20, 2005
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- 852
y=3x^2-6x-5
a second order equation is a conic section
we will complete the square. first rewrite
y=[3x^2-6x]-5
y=3[x^2-2x]-5 complete the square
y=3[x^2-2x+1]-3-5
y=3[x-1]^2-8
a parabola, open up, vertex at 1,-8 answer
you can plot and find the intercepts
Arthur
a second order equation is a conic section
we will complete the square. first rewrite
y=[3x^2-6x]-5
y=3[x^2-2x]-5 complete the square
y=3[x^2-2x+1]-3-5
y=3[x-1]^2-8
a parabola, open up, vertex at 1,-8 answer
you can plot and find the intercepts
Arthur
Graph this function
y=3x^2-6x-5
Label each axis and all intercepts.
You haven’t told us what you’ve tried.
This is a parabola that opens “upwards.”
Several approaches are possible. For one, the vertex has an x value of “-b/2a”. After you find that x value, plug it into the equation and find the y value of the vertex.
Secondly, you can plug in 0 for x and immediately see that the y intercept is –5.
Alternatively, you can try factoring the function and find the x intercepts; this one does not factor though.
To find x intercepts, set y = 0 and solve for x using the quadratic formula.
If you do not like the “-b/2a” approach, you can complete the square and convert the equation into “vertex” form. (Arthur has done this for you.) This will also show you where the vertex is.
As a last resort, you can create an x-y table and calculate (x,y) pairs and plot them until you see the shape of the graph.