How do you find the vertex of a quadratic equation in standard form?
2 answers:
Answer:
Step-by-step explanation:
The standard form of a quadratic equation is ax² + bx + c, where<em> a</em> ≠ 0.
Given that the <u>axis of symmetry </u>occurs at <em>x</em> = <em>h,</em> then we can assume that the <em>h</em> coordinate of the vertex is the same as the x-coordinate in an ordered pair, (x, y).
In order to find the vertex, (h, k), use the following formula to solve for the value of <em>h</em>:
.
To demonstrate this concept, let's say that we're given the following quadratic equation: 2x² + 8x + 8, where a = 2, b = 8, and c = 8. Substitute the values of a and b into the given equation for solving the x-coordinate (<em>h</em>) of the vertex:
Therefore, <em>h</em> = -2.
Next, substitute the value of <em>h</em> = -2 into the given quadratic equation in order to solve for its corresponding y-coordinate (<em>k </em>) of the vertex:
<em>k = </em>2x² + 8x + 8
where: a = 2, b = 8, and c = 8
<em>k = </em>2(-2)² + 8(-2) + 8
<em>k </em>= 2(4) - 16 + 8
<em>k </em>= 8 - 16 + 8
<em>k </em>= 0
Therefore, the vertex of the quadratic equation, <em> </em>2x² + 8x + 8 is (-2, 0).
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<h2>Answer:</h2>
The correct answer is: Option: A
A. 85, 78, 80, 108, 46, 66, 68, 82, 72, 68
<h2>Step-by-step explanation:</h2>It is given that:
The whisker ranges from 66 to 85.
The box ranges from 68 to 82 with the vertical bar inside the box at 75.
- Hence, the minimum value of the box plot is: 66
- Maximum value of box plot is: 85
Also,
- The first quartile or the lower quartile i.e.
is: 68
- The middle quartile or median i.e.
is: 75
- The upper quartile or third quartile i.e.
is: 82
Also, it is given that:
One dot mark above forty-six.
One dot mark above one hundred and eight.
A)
On arranging the data in increasing order after removing outliers 46 and 108 we have:
66 68 68 72 78 80 82 85
Hence, from this data we have:
Minimum value=66
maximum value=85
As all the values matches the value defined.
Hence, this option is correct.
B)
On arranging the data in increasing order after removing 46 and 108 we have:
66 68 68 70 70 80 82 85
Hence, from this data we have:
Minimum value=66
maximum value=85
As the value of .
Hence, this option is incorrect.
C)
On arranging the data in increasing order after removing 46 and 108 we have:
66 68 72 78 80 80 82 85
Hence, from this data we have:
Minimum value=66
maximum value=85
As the value of do not match.
Hence, this option is incorrect.
D)
On arranging the data in increasing order after removing 46 and 108 we have:
66 68 68 72 78 80 80 85
Hence, from this data we have:
Minimum value=66
maximum value=85
As the value of do not match.
Hence, this option is incorrect.