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xenn [34]
3 years ago
5

(0,-4),(1,0),(2,2) find a quadratic function in standard form for each set of points.

Mathematics
1 answer:
Sphinxa [80]3 years ago
4 0
We are given the points
 <span>(0,-4),(1,0),(2,2)
The standard form a quadratic function (in terms of x) is
y = Ax2 + Bx + C
Subsitute the points
-4 = 0 + 0 + C
C = -4

0 = A + B - 4

2 = 4A + 2B - 4

Solve for A and B
A = -1
B = 5

The function is
y = -x2 + 5x - 4</span>
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vova2212 [387]

The equation for the table is y = 2.5 x

Step-by-step explanation:

The table is:

  • x  →  2    :    5.6    :    7    :    8
  • y  →  5    :    14      :  17.5  :    20

Lets check if the table represents the linear relation by find the ratio between the change of each two consecutive y-coordinates and the change of their corresponding x-coordinates

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∵ \frac{17.5-14}{7-5.6}=\frac{3.5}{1.4}=2.5

∵ \frac{20-17.5}{8-7}=\frac{2.5}{1}=2.5

∴ The rate of change between each two points is constant

∴ The table represent a linear equation

The form of linear equation is y = m x + b, where m is the rate of change and b is value y when x = 0

∵ m = 2.5

- Substitute it in the form of the equation

∴ y = 2.5 x + b

- To find b substitute x and y by the coordinates of any point

  in the table above

∵ x = 2 and y = 5

∴ 5 = 2.5(2) + b

∴ 5 = 5 + b

- Subtract 5 from both sides

∴ 0 = b

∴ y = 2.5 x

The equation for the table is y = 2.5 x

Learn more:

You can learn more about the linear equations in brainly.com/question/4326955

#LearnwithBrainly

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