What type of slope does the line have? Positive Negative Zero Undefined
2 answers:
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Answer:
a. y-intercept:(0, -6), x-intercepts: (3, 0) and (-2, 0). vertex: (0.5, -6.25)
b. y-intercept: (0, 6), x-intercepts(3, 0) and (-2, 0). vertex: (0.5, 6.25)
Step-by-step explanation:
a:
So finding the y-intercept is really easy and is simply when x=0. If you plug in 0 as x it makes which simplifies to -6, which is the y-intercept. As for the x-intercepts you can calculate that by using the quadratic equation
. In this case a=1, b=-1, c=-6. So plugging those values in you get
, which simplifies to
. This gives you the x-intercepts 6/2 and -4/2 which are 3 and -2. The vertex can be calculated by manipulating the equation so it's in the form of
where (h, k) is the vertex of the parabola. This is done by moving c to the other side and then completing the square and the isolating y. So the first step will be
Move c to the other side
Complete the square by adding (b/2)^2
Rewrite as square binomial
Isolate y
(h, k) = 0.50, -6.25 which is the vertex
b: To identify the y-intercept you plug in 0 as x which will only leave c which in this case is 6 which is the y-intercept. (0, 6). To identify the x-intercepts you can simplify plug in the values a, b, c into the quadratic equation which was stated in the previous answer. In this case a, b, c = -1, 1, 6. Plugging these values in gives the equation . which simplifies to
which gives the values -2 and 3. To find the vertex it's the same process as before
Factor out -1
Add 6 to both sides (on the left side add -6 since -1 was factored out).
Complete the square by adding (b/2)^2 to both sides (add -(b/2)^2 to left side since -1 was factored out)
Rewrite as square binomial
Add 6.25 to both sides
(h, k) = (0.50, 6.25)
When you graph the parabolas you'll notice there just flipped relative to the x-axis. This can be deduced by simply looking at the two equations, since the two equations have the same absolute value coefficients, the signs are just different, and more specifically they're all opposite. If you took the first equation and multiplied the entire right side by -1 you would get the same equation. And since that equation really represents the value of y (since it's equal to y) you're reflecting it across the x-axis.
Answer:
Explanation:
The number of emails is multiplied by <em>4</em> every <em>9.1 weeks.</em>
Thus, since <em>Tobias initially sent the chain letter to 37 friends</em>, the number of letters will grow as per this geometric series:
Start: 37 letters
- In 9.1 weeks: 37 × 4
- In 2 × 9.1 weeks: 37 × (4)²
- In 3 × 9.1 weeks: 37 × (4)³
As you see, the exponent is the number of weeks divided by 9.1
Thus, if your variable is the number of weeks, t, then the exponent is t/9.1
And the exponential function, P(t) will be: