What is the equation of the following graph?
1 answer:
From the diagram, Vertex =(2,3)
So, (h,k)=(2,3)
So, h=2 and k=3
The equation of parabola is
p is the distance of directrix or focus from vertex.
As directrix is
y=8=k-p=3-p
So, 8=3-p
Let, us subtract 3 from both sides, we get
8-3=3-3-p
5=-p
or p=-5
So, h=2,k=3 and p=-5
So, the equation of parabola is
=4(-5)(y-3)
Equation of graph is
(x-2)^2=-20(y-3)
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Part (a) asked for the equation of the line in y = mx+b form
That would be y = -2x+9
This is because each time y goes down by 2, x goes up by 1. We have slope = rise/run = -2/1 = -2. This indicates that the height of the candle decreases by 2 inches per hour. The slope represents the rate of change.
The initial height of the candle is the y intercept b value. So we have m = -2 and b = 9 lead us from y = mx+b to y = -2x+9
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Part (b) then asks you to graph the equation. Because this is a linear equation, it produces a straight line. We only need 2 points at minimum to graph any line. Let's plot (0,9) and (1,7) on the same xy grid. These two points are the first two rows of the table. Plot those two points and draw a straight line through them. The graph is below
