Use the quadratic formula to solve x2 – 3x - 2 = 0.
2 answers:
Answer:
2.5 or 3.5
Step-by-step explanation:
The quadratic formula is .
a, b, and c are determined by the terms in the formula ax^2 + bx + c
They gave you the equation x^2 - 3x - 2, which fits that formula. a is 1, b is -3, and c is -2. So plug those values into the equation:
So x is 3 plus or minus -1/2. 3 plus -1/2 is 2.5
3 minus -1/2 is 3.5
So the 2 possible x values are 2.5 and 3.5.
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The given polynomial function has 1 relative minimum and 1 relative maximum.
<h3>What are the relative minimum and relative maximum?</h3>- The relative minimum is the point on the graph where the y-coordinate has the minimum value.
- The relative maximum is the point on the graph where the y-coordinate has the maximum value.
- To determine the maximum and the minimum values of a function, the given function is derivated(since the maximum or minimum is obtained at slope = 0)
The given function is
f(x) = 2x³ - 2x² + 1
derivating the above function,
f'(x) = 6x² - 4x
At slope = 0, f'(x) = 0 (for maximum and minimum values)
⇒ 6x² - 4x = 0
⇒ 2x(3x - 2) = 0
2x = 0 or 3x - 2 = 0
∴ x = 0 or x = 2/3
Then the y-coordinates are calculated by substituting these x values in the given function,
when x = 0;
f(0) = 2(0)³ - 2(0)² + 1 = 1
So, the point is (0, 1)
when x = 2/3;
f(2/3) = 2(2/3)³ - 2(2/3)² + 1 = 19/27
So, the point is (2/3, 19/27)
Since y = 1 is the largest value, the point (0, 1) is the relative maximum for the given function.
So, y = 19/27 is the smallest value, the point (2/3, 19/27) is the relative minimum for the given function.
Thus, option A is correct.
Learn more about the relative minimum and maximum here:
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Answer:
Step-by-step explanation:
The equation of a linear function in a slope-intercept form is written as
where
m is the slope of the line
q is the y-intercept
We proceed as follows. First of all, we find the y-intercept, which is the value of y at which the line touches the y-axis.
From the graph, we see that this occurs at y = 4, therefore the y-intercept is
Now we have to find the slope. We do that by choosing two points along the line, with coordinates and
and by using the equation
Here we take the two points:
(0,4)
(-8,0)
So the slope is
Therefore, the equation of the line is