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3 years ago

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The graph of y = 4x^2 - 4x - 1 is shown use the graph to find estimates for the solutions of a and b

1 answer:

8_murik_8 [283]3 years ago

5 0

Answer:

a) -0.25 and 1.25

b) -0.5 and 1.5

Step-by-step explanation:

a) For 4x^2-4x -1 = 0

What we have to do here is to simply find he points on the x-axis in which the graph crosses it

we have this as;

approximately-0.5 and 1.5

what we are saying is that the plot crosses the x-axis at x = -0.25 and x = 1.25

ii) what we have to do here is to find the point at which y = 2

After finding this point, we trace it to the plot sideways, before we trace to the x-axis

By tracing, we have the crossing on the x-axis at these points at -0.5 and 1.5

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Step-by-step explanation:

Given

Interval: (0,3)

See attachment for functions f(x), g(x) and h(x)

Required

Order from fastest to slowest decreasing average rate of change

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$Rate = \frac{f(b) - f(a)}{b - a}$

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$(a,b) = (0,3)$

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$a = 0\\b=3$

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$f(x) = 16(\frac{1}{2})^x$

$Rate = \frac{f(b) - f(a)}{b - a}$

$Rate = \frac{f(3) - f(0)}{3 - 0}$

$Rate = \frac{f(3) - f(0)}{3}$

Calculate f(3) and f(0)

$f(x) = 16(\frac{1}{2})^x$

$f(3) = 16(\frac{1}{2})^3 = 16 * \frac{1}{8} = 2$

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So:

$Rate = \frac{f(3) - f(0)}{3}$

$Rate = \frac{2 - 16}{3}$

$Rate = -\frac{14}{3}$

For g(x)

$Rate = \frac{g(b) - g(a)}{b - a}$

$Rate = \frac{g(3) - g(0)}{3 - 0}$

$Rate = \frac{g(3) - g(0)}{3}$

From the table of g(x)

$g(3) = 1$

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So:

$Rate = \frac{1 - 27}{3}$

$Rate = -\frac{26}{3}$

For h(x)

$Rate = \frac{h(b) - h(a)}{b - a}$

$Rate = \frac{h(3) - h(0)}{3 - 0}$

$Rate = \frac{h(3) - h(0)}{3}$

From the graph of h(x)

$h(3) = -3$

$h(0) = 4$

So:

$Rate = \frac{-3 - 4}{3}$

$Rate = -\frac{7}{3}$

So, the calculated rates of change are:

$f(x) = -\frac{14}{3}$ $= -4.67$

$g(x) = -\frac{26}{3}$ $=-8.67$

$h(x) = -\frac{7}{3}$ $=-2.33$

By comparison:

From the fastest decreasing to slowest, the order is: <em>g(x), f(x) and h(x)</em>

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