Determine the intercepts of the line. y = 5 x − 1 3 y=5x−13
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<h3>Answer: g(x)</h3>
See diagram below.
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Explanation:
The highest point on f(x) is the vertex point since the leading coefficient is negative. The vertex is located at (h,k)
For the general parabola y = ax^2 + bx + c, we can define h to be
h = -b/(2a)
In this case, we plug in a = -2 and b = 8 to find h to be...
h = -b/(2a)
h = -8/(2*(-2))
h = -8/(-4)
h = 2
Then the value of k is equal to f(h). So we plug x = 2 into the f(x) function to get
f(x) = -2x^2 + 8x - 1
f(2) = -2(2)^2 + 8(2) - 1
f(2) = -2(4) + 8(2) - 1
f(2) = -8 + 16 - 1
f(2) = 8 - 1
f(2) = 7
This means k = 7
So the vertex for f(x) is at (h,k) = (2,7)
The max value of f(x) is f(x) = 7 which is the same as y = 7.
The graph shows the highest point is at (0,10). The highest point of g(x) is when y = 10. So this is the largest g(x) can get. We only are concerned with output values when we want to maximize whatever the function is.
Therefore, g(x) produces the larger maximum value compared to f(x).
We can see that if we were to graph both f(x) and g(x) together. The g(x) curve peaks higher compared to f(x).
The diagram is shown below. I used GeoGebra to make the graph, though you could use Desmos or a TI calculator (or similar) if you want.