Write the equation of a parabola in standard form that contains the points (0, 0), (-1, -5), and (2, -2)

  y = -2x² + 3x

Step-by-step explanation:

The y-intercept of 0 tells you the constant is zero.

You can find the coefficients "a" and "b" in the form

  y = ax² +bx +0

by substituting the data points that are not the y-intercept.

For x=-1, ...

  -5 = a(-1)² +b(-1) = a - b

For x=2, ...

  -2 = a(2)² +b(2) = 4a +2b

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These two equations can be solved by your favorite method. Here's one way:

You can divide the second equation by 2 and add the first:

  (-2)/2 +(-5) = (4a +2b)/2 +(a -b)

  -6 = 3a

  -2 = a

Then you can use either equation to find b.

  -5 = -2 -b . . . substitute for "a" in the first equation

  b = 3 . . . . . . add b+5

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Now, you know the quadratic is

  y = -2x² +3x

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Alternate solution

You can let your graphing calculator or spreadsheet program tell you the equation of a quadratic regression using these points. The attached shows one such result. (It is the same as above.)

y = -2x² + 3x

Step-by-step explanation:

The standard form of a quadratic equation is: y = ax² + bx + c

Input the x, y coordinates provide to create three equations. Then solve the system of equations

(0, 0) → 0 = a(0)² + b(0) + c

            0 =   0    +   0   + c

            0 = c

(-1, -5) and c = 0 → -5 = a(-1)² + b(-1) + 0

                             -5 =    a     +   -b

(2, -2) and c = 0 → -2 = a(2)² + b(2) + 0

                             -2 =  4a    +  2b

-5 =   a -   b  →  2(-5 = a  -  b)  →  -10 = 2a - 2b

-2 = 4a + 2b → 1(-2 = 4a + 2b) → -2 = 4a + 2b

                                                   -12 = 6a

                                                   ÷6   ÷6  

                                                    -2 = a

-5 = a - b

-5 = -2 - b

-3 = -b

3 = b

a = -2, b = 3, c = 0  →   y = -2x² + 3x + 0

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d

we have the parent function given by,

1. the function is translated 5 units to the left.

so, we get,   becomes

2. the function is translated 5 units to the right.

so, we get,   becomes

3. the function is translated 5 units upwards.

so, we get,   becomes

4. the function is translated 5 units downwards.

so, we get,   becomes

5. the function is reflected across x-axis.

so, we get,   becomes

6. the function is reflected across y-axis.

so, we get,   becomes .

step-by-step explanation:

mark brainliest.