2. order the group of parabolas from widest to narrowest

y = 1/4x 2, y = -1/2x 2, y = 3/2x 2

5. how is the graph of y = -4x 2 – 5 different from the graph of y = -4x 2?

6. what is the value of c such that: x2 + 14x + c, is a perfect-square trinomial?

7. the table shows the estimated number of deer living in a forest over a five-year period. which type of function best models the data? write an equation to model the data.
year estimated population
0 100
1 79
2 62
3 49
4 39

a. linear; y = 0.79x + 100
b. quadratic; y = 100x2 + 0.79
c. exponential; y = 100 * 0.79x
d. quadratic; y = 0.79x2 + 100

2.

5. y = -4x² shifted 5 units downwards.

6. Option C. c = 49

7. Option D. quadratic; y = 0.79x² + 100

Step-by-step explanation:

2. In a given quadratic equation of parabola y = ax² + bx + c, higher the coefficient of x² that is a, narrower will be the parabola.

Therefore, out of three equations of parabola will be the narrowest.

5. Graph y = -4x² is passing through origin (0, 0). Now this graph has been shifted 5 units downwards to create a transformed form of y = - 4x² - 5.

6. The given trinomial is (x² + 14x + c). We have to find the value of c for which his trinomial becomes a perfect square.

x² + 14x + c = x² + 2(7)x + c

= x² + 2(7)x + 49

= (x + 7)² [ since (a + b)² = a² + 2ab + b². Here a = x and b = 7 ]

Therefore, c = 49 is the answer.

7. We have to find the type of function which models the data given in the table.

For Linear function.

There should be common difference in the y - values.

79 - 100 = -21

62 - 79 = -17

49 - 62 = -13

Since there is no common difference so data don't represent the linear function.

For quadratic equation.

Difference of difference values of y should be same.

As we have calculated above

Difference of the terms given in the table are -21, -17 and -13

So difference of difference will be

-21 - (-17) = -4

(-17) - (-13) = -4

Finally we find that difference of difference is same as (-4).

Therefore, equation that models the data is QUADRATIC.

y = 0.79x² + 100 [since at x = 0, value of y = 100, so y - intercept is 100]

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