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

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

Part E : 5

Step-by-step 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 (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  

Therefore, the x-intercept will be at (4,0) and . (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  

(Answer)

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: