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1 answer:
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Answer:
The answer to your question is:
Step-by-step explanation:
Data
f(x) = -2x² + 8x - 2
Process
-2x² + 8x = y + 2
-2(x² - 4x + 4) = y + 2 - 8
-2(x - 2)² = y - 6
(x - 2)² = 1/2 (y - 6)
Vertex = (2, 6)
Axis of symmetry = x = 2
y-intercept
f(0) = -2(0)² + 8(0) - 2
f(0) = 0 + 0 - 2
f(0) = -2
Domain (-∞, ∞)
Range (-∞, 6]
See the graph below
Answer:
1a. y-intercept: 12
1b. slope: -3/2
1c. equation: y = -3/2x +12
2a. y-intercept: -9
2b. slope: 2
2c. equation: y = 2x -9
Step-by-step explanation:
<h3>1.</h3>A) We observe the pattern to be <em>x-values in the table increase by 2, while y-values in the table decrease by 3</em>. We notice the first x-value is 2, so extending the table upward to x=0 would tell us the y-intercept. That is, adding 3 to the first y-value will give the y-intercept as (x, y) = (0, 12).
B) We have already observed that the "rise" (change in y) is -3 for each "run" (change in x) of 2. The slope is the ratio of these changes:
slope = m = rise/run = -3/2
C) From the above, we know that m=-3/2 and b=12. Putting these values into the equation for the line gives ...
y = -3/2x +12
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<h3>2.</h3>A) We observe the pattern to be <em>y-values increase by 2 while x-values increase by 1</em>. As before, we can find the point that would go before the first one shown in the table. It will have an x-value of 0 and a y-value of -9.
the y-intercept is -9
the slope is 2/1 = 2
the equation is y = 2x -9
