graphing quadratics?

Question

y = 2x2 - 10x - 1

y = 4x2 + 12x + 9

y = x2 + x + 1

y = x2 -5x + 4

Answer 1

In case you didn't notice, it is really hard to graph in a text format like this one. But here is what YOU can do to graph the equations.

First, find the line of symmetry.
In y = 2x^2 - 10x - 1,. A = 2, B = -10, and C = -1
The line of symmetry is the equation x = -B/2A, or in this case,
x = -(-10)/2(-2)
x = 5/2

The vertex (in this case the minimum point on the graph) is on this line. So find the y-value of the vertex.
y = 2x^2 - 10x - 1
y = 2(5/2)^2 - 10(5/2) - 1
y = 25/2 - 25 - 1
y = 12.5 - 26
y = -13.5

So the vertex is (2.5, -13.5).

Then find some more points on the graph by plugging in values close to x = 2.5. (Try x = 0, 1, 2, 3, 4). Graph all of these resulting points. Also, knowing the line of symmetry, the y value for x = 2 and x = 3 should be identical.
Finally, connect these points with a smooth curve.

Then repeat these steps for each of the other problems!
I hope this helps!

Answer 2

Do you really expect someone to graph these for you?

Some hints: If the coefficeint of the x^2 term is positive, the parabola opens up on the positive side. The roots of the equation are x-intercepts; if the roots are imaginary, the curve will not cross the y-axis. The minimum point of the curve ax^2+bx+c=y has an x-coordinate of -b/2a.

Answer 3

First rewrite the funcions into this form:

2*pow(x#2)-10*x-1
4*pow(x#2)+12*x+9
pow(x#2)+x+1
pow(x#2)-5*x+4

Then visit the webpage
http://rechneronline.de/function-graphs/
and enter the functions. You will see the graphs.
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