Josh is preparing for an exam by completing practice tests that have different numbers of questions. For each practice test, he
notes the number of questions and the time it takes him to complete the test.
Next, Josh creates a scatter plot and draws a trend line to fit the data. To see how well the trend line represents the data, Josh draws black lines to represent the distance each data point lies away from the trend line.
What is the sum of the residuals for all the points?
A. 97
B. 19
C. 39
D. 58
Next, Josh creates a scatter plot and draws a trend line to fit the data. To see how well the trend line represents the data, Josh draws black lines to represent the distance each data point lies away from the trend line.
What is the sum of the residuals for all the points?
A. 97
B. 19
C. 39
D. 58
2 answers:
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NOTES:
Given a quadratic function in standard format (y = ax² + bx + c), the direction of the parabola is as follows:
- if "a" is positive, then opens UP
- if "a" is negative, then opens DOWN
Given a quadratic function in standard format (y = ax² + bx + c), the vertex can be found as follows:
- the Axis Of Symmetry (x-value) is: x =
- y-value is found by plugging in the AOS for "x" in the equation
****************************************************************************************
1) y = x² + 11x + 24
- a = +1 so the parabola opens UP
- x =
=
=
- y =
+ 11
+ 24 =
- vertex
,
is in Quadrant 3 and is below the x-axis
This COULD be the graph of the rain gauge.
The graph should contain the vertex, x-intercepts (-3, 0) and (-8, 0), and y-intercept (0, 24)
******************************************************************************************
2) y = -x² - 6x - 8
- a = -1 so the parabola opens DOWN
- x =
=
= -3
- y = -(-3)² - 6(-3) - 8 = -9 + 18 - 8 = 1
- vertex (-3, 1) is in Quadrant 2 and is above the x-axis
This could NOT be the graph of the rain gauge.
The graph should contain the vertex, x-intercepts (-2, 0) and (-4, 0), and y-intercept (0, -8)
******************************************************************************************
3) y = x² - 2x + 3
- a = 1 so the parabola opens UP
- x =
=
= 1
- y = (1)² - 2(1) + 3 = 1 - 2 + 3 = 2
- vertex (1, 2) is in Quadrant 1 and is above the x-axis
This could NOT be the graph of the rain gauge.
The graph should contain the vertex, y-intercept (0, 3), and its mirror image (2, 3). <em>There are no x-intercepts</em>
******************************************************************************************
4) y = x² + 4x + 4
- a = 1 so the parabola opens UP
- x =
= -2
- y = (-2)² + 4(-2) + 4 = 4 - 8 + 4 = 0
- vertex (-2, 0) is in Quadrant 2 and is on the x-axis
This COULD be the graph of the rain gauge.
The graph should contain the vertex, y-intercept (0, 4), and its mirror image (-4, 4). <em>The x-intercept is the vertex.</em>
Compared to the other four graphs, this is most likely the equation for the rain gauge!
******************************************************************************************
5) y = 3x² + 21x + 30
- a = +3 so the parabola opens UP
- x =
=
- y = 3
+ 21
+ 30 =
- vertex
,
is in Quadrant 3 and is below the x-axis
This COULD be the graph of the rain gauge.
The graph should contain the vertex, x-intercepts (-2, 0) and (-5, 0), and y-intercept (0, 30)
*******************************************************************************************
The formula of a slope:
We have the points (2, 5) and (4, 10). Substitute:
This means that 2.5mm of rain falls every hour