Answer:
2. \(y=\frac{3}{4}x^{2}\)
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 \(y=\frac{3}{4}x^{2}\) 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]
