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barxatty [35]
4 years ago
5

Last question. Use the table of values that represent points on the graph of a quadratic function. By determining the vertex and

axis of symmetry, find the general form of the equation of the quadratic function.
x = -2, -1, 0, 1, 2
y = 1, 0, 1, 4, 9
Mathematics
1 answer:
galben [10]4 years ago
6 0

Examining the y-values shows that all of the given y-values are perfect squares. Further, the graph dips at first, reaches a minimum (-1,0) and then increases as does the second power of x.

This is sufficient info on which to base the conclusion that the vertex of this parabolic function is at (-1,0), and that the axis of symmetry (which goes thru the vertex) is x = -1.

The most basic form of the equation of a parabola is y = x^2. The graph is that of a parabola and opens up. The vertex is (0,0) and the axis of symmetry is x=0.

In this particular case, the vertex has been translated 1 unit to the left. The corresponding equation of this "new" parabola is y = (x+1)^2. Note that (2,9) (one of the points given in the table) satisfies this equation:

9 = (2+1)^2.

The desired equation is y = (x+1)^2.

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Answer:

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Step-by-step explanation:

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5 0
2 years ago
Which equation represents the function graphed on the
Vesna [10]
Since you haven't provided the graph, I'll explain each one and you choose the one suiting your given.
The parent modulus function is:
g(x) = |x|
It is centered at the origin and opens upwards.
A coefficient inside the modulus |x+k| means that the function is shifted along the x-axis
If "k" is positive, the shift will be to the left. If "k" is negative, the shift will be to the right.
A coefficient outside the modulus |x| + h means that the function is shifted along the y-axis
If "h" is positive, the shift will be upwards. If "h" is negative, the shift will be downwards.
Now, let's check each of the options:
g(x) = |x+4| - 2 :
This function is shifted 4 units to the left and 2 units down. It will be centered at (-4,-2). Check the blue graph in the attachment.
g(x) = |x-4| - 2 :
This function is shifted 4 units to the right and 2 units down. It will be centered at (4,-2). Check the black graph in the attachment.
g(x) = |x-2| - 4 :
This function is shifted 2 units to the right and 4 units down. It will be centered at (2,-4). Check the red graph in the attachment.
g(x) = |x-2| + 4 :
This function is shifted 2 units to the right and 4 units up. It will be centered at (2,4). Check the green graph in the attachment.
All 4 graphs are shown in the attached picture.
Hope this helps :)



4 0
3 years ago
In the equation 3x^2-10x=8 please solve for x and show work ty !
RSB [31]

Answer:

x=4,-2/3

Step-by-step explanation:

To solve for x, we first subtract 8 from both sides.

So 3x^2-10x-8=0

Using the quadratic formula, we get

X=(10+sqrt(100+96))/6 or x = (10-sqrt(100+96))/6

So x=(10+14)/6 or x=(10-14)/6

So x=4 or x=-2/3.

8 0
3 years ago
Read 2 more answers
Balance the equation
loris [4]

On the right side, there are

• 2•2 = 4 atoms of Nb

• 2•5 = 10 atoms of O

so among the reactants on the left, the reaction is balanced as

4 Nb + 5 O₂   →   2 Nb₂O₅

7 0
2 years ago
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