How do I figure out problems similar to the following by graphing y = 2x2 + 3?
Find the y intercept, which means setting x=0, and the y intercept in this case is (0,3)
Find the x intercepts using the quadratic equation or factoring- There is no x-intercepts in that problem
Find the axis of symmetry, which is to find the min or the max otherwise known as vertex, in this case it would be the same as the y-intercept
Look at the sign to see if it's concave up or down
I think thats basically it to graph simple parabolas like the example you gave.
Easier way...plug in x values...or use the calculator
I assume you know what vertex, and setting x=0 and y=0 does since this is in the pre-calc section
The basic equation of a parabola is
So to find the vertex of the equation you gave , you would do x=-b/2a, and in this cause there is no b, which means it is 0 so the x value of the vertex would be x=0/4=0 and plug in 0 for x in the equation you would get the vertex at (0,3).
Now that you have the vertex it's time to find the x intercept. To find the x-intercept you would either use the quadratic equation or factoring it if possible. The equation equation is:
Now solve for x. Whatever you get for x should the x intercepts..which I assume you know what it is. I don't think there is any x-intercepts in this case.
Now for the y intercept just set x=0 in the equation. Because that means when x=0, y=?. In this case when you set x=0, y will be 3 right?
I understand everything in this part...
But I don't understand how you got the vertex....Easier way...plug in x values...or use the calculator
I assume you know what vertex, and setting x=0 and y=0 does since this is in the pre-calc section
The basic equation of a parabola is
So to find the vertex of the equation you gave , you would do x=-b/2a, and in this cause there is no b, which means it is 0 so the x value of the vertex would be x=0/4=0
-b/2a is the x value of the vertex because it is also the axis of symmetry for the parabola. To get the vertex, you plug in the x and you will get the y-value so the vertex would be (-b/2a, f(-b/2a)) with f(x) = y. If you are looking for where did I get -b/2a or how to derivative it, read this webpage
Anything in the form of where m is the slope and b is the y-intercept.
It is linear because when you graph it you do not get a curve. You get a straight line.
And to do this really easily just plug in x-values, from that you can get the y-values and then plot. Then do a simple connect the dots. You should get a pretty skinny curve with the vertex at You can find the vertex as linnus said by doing You can use this only if it is in the form