Question 20187: graph (Show your work)
y=16-x^2
Thanks a bunch
Answer by mmm4444bot(95)   (Show Source):
You can put this solution on YOUR website! Hello There:
First of all, you should recognize the expression on the right side of the equals sign to be a quadratic expression. In other words, it's in the form of:
y = a*x^2 + b*x + c
Hopefully you know that the graph is going to be a parabola.
We have:
y = -x^2 + 16
Right away, we see that the parabola opens downward because the value of "a" is negative.
There are formulas for the x- and y-coordinates of the vertex point.
x-coordinate = -b/(2*a)
y-coordinate = c - b^2/(4*a)
Our equation shows that:
a = -1
b = 0
c = 16
Substitute these values into the formula above to find that (0, 16) is the vertex point.
The expression 16 - x^2 can be factored as a difference of squares.
(4 + x)*(4 - x)=0
So, the x-intercepts of the graph are (-4, 0) and (4, 0).
Pick some other values of x, and find the corresponding values of y to get a few more points to plot. Then draw the parabola using a smooth curve that goes through all of the points that you have plotted.
~ Mark
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