Answer:
A): f(x) = (x – 1)² + 2
Step-by-step explanation:
The quadratic function, f(x) = (x – 1)² + 2 is in <u>vertex form</u>: y = a(x - h)² + k, where:
- The vertex of the graph is (h,k).
- The value of <em>a</em> determines whether the graph opens up or down. If <em>a</em><em> </em>is <u>positive</u>, the graph opens up and the vertex is its minimum point. If <em>a </em>is <u>negative</u>, then the graph opens down, and the vertex is its maximum point.
- The value of <em>h</em> determines how far left or right the parent function is translated.
- The value of<em> k</em> determines how far up or down the parent function is translated.
The function, f(x) = (x – 1)² + 2, provides the pertinent information that allows us to determine the parabola's <u>minimum value</u>, as the value of <em>a</em> is a <u>positive</u>, which implies that the parabola is <em>upward facing</em>, and the vertex, (1, 2) is the minimum point.
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Answer:
Step-by-step explanation:
<em><u>The correct question is</u></em>
The sum of three consecutive even integers is -72. what are the three numbers
Let
x ----> the first consecutive even integer
x+2 ----> the second consecutive even integer
x+4 ----> the third consecutive even integer
we know that
solve for x
so
therefore
the numbers are
This is false because the confection of a determination is native
Answer:
x=10, y=25
Step-by-step explanation:
First, in a trapezoid, the two angles on the same leg (the legs are the opposite sides that are not parallel) add up to 180 degrees. Therefore, 4y as well as (2y+3x) are supplementary. We can write this out as
4y + (2y+3x) = 180
6y+3x = 180
Next, the angles of a triangle add up to 180 degrees. Therefore, as the angles 2y, 4y, and (5x-20) make up a triangle, they add up to 180 degrees. We can write this as
4y + 2y + (5x-20) = 180
6y + 5x -20 =180
Our two equations are thus
6y + 5x - 20 = 180
6y + 3x = 180
If we subtract 6y from both sides in each equation, we can say
5x - 20 = 180-6y
3x = 180-6y
Therefore, we can write
5x-20 = 180-5y = 3x
5x-20=3x
subtract 3x from both sides to make all x variables on the same side
2x-20 = 0
add 20 to both sides to isolate the x and its coefficient
2x = 20
divide both sides by 2 to isolate x
x = 10
Therefore,
x = 10
6y + 3x = 180
6y + 30 = 180
subtract 30 from both sides to isolate the y and its coefficient
6y = 150
y = 25
