Question

50 points can someone check over my answers were doing quadratic functions and things like that thanks so much

Answer 1

All real numbers less than or equal to 4.

Part B : f(x) = x² + 3x - 40

Part C : a + b = 1

Part D : (4,0) and

Part E : 5

Answer 2

Part A : All real numbers less than or equal to 4.

Part B : f(x) = x² + 3x - 40

Part C : a + b = 1

Part D : (4,0) and
`(-(5)/(2), 0)`

Part E : 5

Explanation:

Part A :

From the given graph the y-value lies between 4 ≥ y ≥ - ∞.

Therefore, the range of the function f(x) = - (x + 5)(x + 1) will be all real numbers less than or equal to 4. (Answer)

Part B :

We have to find the function which has real zeros at x = - 8 and x = 5.

Now, (x + 8) and (x - 5) will be the factors of the quadratic function and hence, f(x) = (x + 8)(x - 5)

⇒ f(x) = x² + 3x - 40 (Answer)

Part C :

If ax² + bx + c = 0 is a quadratic equation having roots α and β then sum of the roots i.e. α + β = - b/a.

Here, the equation x² - x - 90 = 0 has roots a and b, then
`a + b = - (- 1)/(1) = 1` (Answer)

Part : D

The x-intercept of the function f(x) = - 2x²- 3x + 20 will be at f(x) = 0.

So, - 2x² + 3x + 20 = 0

⇒ - 2x² + 8x - 5x + 20 = 0

⇒ (x - 4)(- 2x - 5) = 0

So, either x = 4 or
`x = - (5)/(2)`

Therefore, the x-intercept will be at (4,0) and
`(-(5)/(2), 0)`. (Answer)

Part : E

(0, -3) and (2,7) are the two ordered pair of the function f(x) = 2x² + x - 3.

Therefore, the rate of change for the interval between x = 0 and x = 2 of the function will be

`(7 + 3)/(2 - 0) = 5` (Answer)