Given:
There are given the quadratic equation:
Explanation:
To find the value of x by using completing the square, first, we need to subtract 59 on both sides of the given equation:
So,
From the given equation:
Now,
Take half of the x term and square it:
So,
From the x term,
Then,
Add 64 on both sides of the above equation.
So,
Hence, an option first is correct:
Now,
From the above square:
Then,
Subtract 8 from both sides of the equation;;
So,
Final answer:
Hence, the value of x is shown below:
Answer: B) different y intercepts; same end behavior
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Explanation:
The graph shows the y intercept is 4 as this is where the green curve crosses the vertical y axis.
The y intercept of g(x) is 6 which can be found by plugging x = 0 into the g(x) function
g(x) = 4(1/4)^x + 2
g(0) = 4(1/4)^0 + 2
g(0) = 6
So we can see the y intercepts are different.
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However, the end behaviors are the same for each function. The left side of f(x) goes up forever to positive infinity. The same is true for g(x). You could use a graphing calculator or a table to see this. As x heads to negative infinity, y goes to positive infinity.
In terms of symbols,
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For the right side of f(x), it slowly approaches the horizontal asymptote y = 2. It never actually reaches this y value. The same happens with g(x). The portion 4(1/4)^x gets smaller but never gets to 0 so overall 4(1/4)^x+2 gets closer to 2. We can say that as x approaches infinity, y approaches 2.
In terms of symbols,